EXHIBIT 4.2(a)
                         REGISTRATION RIGHTS AGREEMENT

          This Registration Rights Agreement, dated as of  June 30, 1999 (this
"Agreement"), between Thermatrix Inc., a Delaware corporation, with principal
executive offices located at 308 North Peters Road, Suite 100, Knoxville,
Tennessee (the "Company"), and The Shaar Fund Ltd. (the "Initial Investor").

          Whereas, upon the terms and subject to the conditions of the
Securities Purchase Agreement dated as of June 30, 1999, between the Initial
Investor and the Company (the "Securities Purchase Agreement"), the Company has
agreed to issue and sell to the Initial Investor (i) 3,000 shares of Series E 8%
Convertible Preferred Stock, par value $.001 per share (the "Preferred Shares")
which, upon the terms of and subject to the conditions of the Company's
Certificate of Designation of Series E 8% Convertible Preferred Stock (the
"Certificate of Designation"), are convertible into shares of the Company's
common stock, par value $.001 per share (the "Common Stock") and (ii) Common
Stock Purchase Warrants (the "Warrants") to purchase shares of Common Stock; and

          Whereas, to induce the Initial Investor to execute and deliver the
Securities Purchase Agreement, the Company has agreed to provide with respect to
the Common Stock issued or issuable in lieu of cash dividend payments on the
Preferred Shares, upon conversion of the Preferred Shares and exercise of the
Warrants certain registration rights under the Securities Act;

          Now, Therefore, in consideration of the premises and the mutual
covenants contained herein, the parties hereto, intending to be legally bound,
hereby agree as follows:

            1.   Definitions

            (a)  As used in this Agreement, the following terms shall have the
meanings:

     (i)    "Affiliate," of any specified Person means any other Person who
     directly, or indirectly through one or more intermediaries, is in control
     of, is controlled by, or is under common control with, such specified
     Person. For purposes of this definition, control of a Person means the
     power, directly or indirectly, to direct or cause the direction of the
     management and policies of such Person whether by contract, securities,
     ownership or otherwise; and the terms "controlling" and "controlled" have
     the respective meanings correlative to the foregoing.

     (ii)   "Closing Date" means the date and time of the issuance and sale of
     the Preferred Shares.

     (iii)  "Commission" means the Securities and Exchange Commission.

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     (iv)   "Current Market Price" on any date of determination means the
     closing bid price of a share of the Common Stock on such day as reported on
     the Nasdaq National Market ("Nasdaq"), or, if such security is not listed
     or admitted to trading on the Nasdaq, on the principal national security
     exchange or quotation system on which such security is quoted or listed or
     admitted to trading, or, if not quoted or listed or admitted to trading on
     any national securities exchange or quotation system, the closing bid price
     of such security on the over-the-counter market on the day in question as
     reported by the National Quotation Bureau Incorporated, or a similar
     generally accepted reporting service, or if not so available, in such
     manner as furnished by any Nasdaq member firm of the National Association
     of Securities Dealers, Inc. selected from time to time by the Board of
     Directors of the Company for that purpose, or a price determined in good
     faith by the Board of Directors of the Company as being equal to the fair
     market value thereof, as the case may be.

     (v)    "Exchange Act" means the Securities Exchange Act of 1934, as
     amended, and the rules and regulations of the Commission thereunder, or any
     similar successor statute.

     (vi)   "Investors" means the Initial Investor and any transferee or
     assignee of Registrable Securities who agrees to become bound by all of the
     terms and provisions of this Agreement in accordance with Section 8 hereof.

     (vii)  "Person" means any individual, partnership, corporation, limited
     liability company, joint stock company, association, trust, unincorporated
     organization, or a government or agency or political subdivision thereof.

     (viii) "Prospectus" means the prospectus (including, without limitation,
     any preliminary prospectus and any final prospectus filed pursuant to Rule
     424(b) under the Securities Act, including any prospectus that discloses
     information previously omitted from a prospectus filed as part of an
     effective registration statement in reliance on Rule 430A under the
     Securities Act) included in the Registration Statement, as amended or
     supplemented by any prospectus supplement with respect to the terms of the
     offering of any portion of the Registrable Securities covered by the
     Registration Statement and by all other amendments and supplements to such
     prospectus, including all material incorporated by reference in such
     prospectus and all documents filed after the date of such prospectus by the
     Company under the Exchange Act and incorporated by reference therein.

     (ix)   "Public Offering" means an offer registered with the Commission and
     the appropriate state securities commissions by the Company of its Common
     Stock and made pursuant to the Securities Act.

     (x)    "Registrable Securities" means the Common Stock issued or issuable
     (i) in lieu of cash dividend payments on the Preferred Shares, (ii) upon
     conversion of the Preferred Shares or (iii) upon exercise of the Warrants;
     provided, however, a share of Common Stock shall cease to be a Registrable
     Security for purposes of this Agreement when it no longer is a Restricted
     Security.

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     (xi)   "Registration Statement" means a registration statement of the
     Company filed on an appropriate form under the Securities Act providing for
     the registration of, and the sale on a continuous or delayed basis by the
     holders of, all of the Registrable Securities pursuant to Rule 415 under
     the Securities Act, including the Prospectus contained therein and forming
     a part thereof, any amendments to such registration statement and
     supplements to such Prospectus, and all exhibits and other material
     incorporated by reference in such registration statement and Prospectus.

     (xii)  "Restricted Security" means any share of Common Stock issued or
     issuable in lieu of cash dividend payments on the Preferred Shares, upon
     conversion of the Preferred Shares or exercise of the Warrants except any
     such share that (i) has been registered pursuant to an effective
     registration statement under the Securities Act and sold in a manner
     contemplated by the prospectus included in such registration statement,
     (ii) has been transferred in compliance with the resale provisions of Rule
     144 under the Securities Act (or any successor provision thereto) or is
     transferable pursuant to paragraph (k) of Rule 144 under the Securities Act
     (or any successor provision thereto), or (iii) otherwise has been
     transferred and a new share of Common Stock not subject to transfer
     restrictions under the Securities Act has been delivered by or on behalf of
     the Company.

     (xiii) "Securities Act" means the Securities Act of 1933, as amended, and
     the rules and regulations of the Commission thereunder, or any similar
     successor statute.

          (b)  All capitalized terms used and not defined herein have the
respective meaning assigned to them in the Securities Purchase Agreement.

          2.   Registration

          (a)  Filing and Effectiveness of Registration Statement.  The Company
shall prepare and file with the Commission not later than 60 days after the
Closing Date, a Registration Statement relating to the offer and sale of the
Registrable Securities and shall use its best efforts to cause the Commission to
declare such Registration Statement effective under the Securities Act as
promptly as practicable but not later than 150 days after the Closing Date,
assuming for purposes hereof a Conversion Price under the Certificate of
Designation of $1.50 per share.  The Company shall not include any other
securities in the Registration Statement relating to the offer and sale of the
Registrable Securities.  The Company shall notify the Initial Investor by
written notice that such Registration Statement has been declared effective by
the Commission within 24 hours of such declaration by the Commission.

          (b)  Registration Default.  If the Registration Statement covering the
Registrable Securities or the Additional Registrable Securities (as defined in
Section 2(d) hereof) required to be filed by the Company pursuant to Section
2(a) or 2(d) hereof, as the case may be, is not (i) filed with the Commission
within 60 days after the Closing Date or (ii) declared effective by the
Commission within 150 days after the Closing Date (either of which, without
duplication, an "Initial Date"), then the Company shall make the payments to the
Initial Investor as provided in the next sentence as liquidated damages and not
as a penalty.  The amount to be paid by the Company to the Initial Investor
shall be determined as of each Computation Date (as defined below), and such
amount shall

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be equal to 2% (the "Liquidated Damage Rate") of the Purchase Price (as defined
in the Securities Purchase Agreement) from the Initial Date to the first
Computation Date and for each Computation Date thereafter, calculated on a pro
rata basis to the date on which the Registration Statement is filed with (in the
event of an Initial Date pursuant to clause (i) above) or declared effective by
(in the event of an Initial Date pursuant to clause (ii) above) the Commission
(the "Periodic Amount") provided, however, that in no event shall the liquidated
damages be less than $25,000; provided, further, however, that if the
Registration Statement is not declared effective by the Commission within 210
days after the Initial Date set forth in clause (ii) above, then the Liquidated
Damage Rate shall increase to 4%; provided, further, however, that the
Liquidated Damage Rate shall increase by 1% for each 30 day period after the
210/th/ day after the Initial Date set forth in clause (ii) above that the
Registration Statement is not declared effective by the Commission. The full
Periodic Amount shall be paid by the Company to the Initial Investor by wire
transfer of immediately available funds within three days after each Computation
Date.

          As used in this Section 2(b), "Computation Date" means the date which
is 30 days after the Initial Date and, if the Registration Statement required to
be filed by the Company pursuant to Section 2(a) has not theretofore been
declared effective by the Commission, each date which is 30 days after the
previous Computation Date until such Registration Statement is so declared
effective.

          Notwithstanding the above, if the Registration Statement covering the
Registrable Securities or the Additional Registrable Securities required to be
filed by the Company pursuant to Section 2(a) or 2(d) hereof, as the case may
be, is not filed with the Commission by the 30th day after the Closing Date, the
Company shall be in default of this Registration Rights Agreement.

          (c)  Eligibility for Use of Form S-3.  The Company agrees that at such
time as it meets all the requirements for the use of Securities Act Registration
Statement on Form S-3 it shall file all reports and information required to be
filed by it with the Commission in a timely manner and take all such other
action so as to maintain such eligibility for the use of such form.

          (d)  In the event the Current Market Price declines to $1.75 per
share, the Company shall, to the extent required by the Securities Act (because
the additional shares were not covered by the Registration Statement filed
pursuant to Section 2(a)), as reasonably determined by the Initial Investor,
file an additional Registration Statement with the Commission for such
additional number of Registrable Securities as would be issuable upon conversion
of the Preferred Shares and exercise of the Warrants (the "Additional
Registrable Securities") in addition to those previously registered, assuming a
Conversion Price of $0.75 per share. The Company shall, to the extent required
by the Securities Act, as reasonably determined by the Initial Investor, prepare
and file with the Commission not later than the 30th day thereafter, a
Registration Statement relating to the offer and sale of such Additional
Registrable Securities and shall use its best efforts to cause the Commission to
declare such Registration Statement effective under the Securities Act as
promptly as practicable but not later than 60 days thereafter. The Company shall
not include any other securities in the Registration Statement relating to the
offer and sale of such Additional Registrable Securities.

          If the Additional Registration Statement is not (i) filed with the
Commission within 30 days after the Decline Date or (ii) declared effective by
the Commission within 90 days after the Decline Date (either of which, without
duplication, an "Additional Registration Date"), then the Company shall make the
payments to the Initial Investor at the Liquidated Damage Rate from the

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Additional Registration Date to the first Additional Computation Date and for
each Additional Computation Date thereafter, calculated on a pro rata basis to
the date on which the Additional Registration Statement is filed with (in the
event of an Additional Registration Date pursuant to clause (i) above) or
declared effective by (in the event of an Additional Registration Date pursuant
to clause (ii) above) the Commission (the "Additional Periodic Amount")
provided, however, that in no event shall the liquidated damages be less than
$25,000; provided, further, however, that if the Additional Registration
Statement is not declared effective by the Commission within 120 days after the
Additional Registration Date set forth in clause (ii) above, then the Liquidated
Damage Rate shall increase to 4%; provided, further, however, that the
Liquidated Damage Rate shall increase by 1% for each 30 day period after the
120/th/ day after the Additional Registration Date set forth in clause (ii)
above that the Additional Registration Statement is not declared effective by
the Commission. The full Additional Periodic Amount shall be paid by the Company
to the Initial Investor by wire transfer of immediately available funds within
three days after each Additional Computation Date.

          As used in this Section 2(d), "Additional Computation Date" means the
date which is 30 days after the Additional Registration Date and, if the
Additional Registration Statement required to be filed by the Company pursuant
to this Section 2(d) has not theretofore been declared effective by the
Commission, each date which is 30 days after the previous Additional Computation
Date until such Additional Registration Statement is so declared effective.

          (e)  (i)  If the Company proposes to register any of its warrants,
     Common Stock or any other shares of common stock of the Company under the
     Securities Act (other than a registration (A) on Form S-8 or S-4 or any
     successor or similar forms, (B) relating to Common Stock or any other
     shares of common stock of the Company issuable upon exercise of employee
     share options or in connection with any employee benefit or similar plan of
     the Company or (C) in connection with a direct or indirect acquisition by
     the Company of another Person or any transaction with respect to which Rule
     145 (or any successor provision) under the Securities Act applies), whether
     or not for sale for its own account, it will each such time, give prompt
     written notice at least 20 days prior to the anticipated filing date of the
     registration statement relating to such registration to the Initial
     Investor, which notice shall set forth such Initial Investor's rights under
     this Section 3(e) and shall offer the Initial Investor the opportunity to
     include in such registration statement such number of Registrable
     Securities as the Initial Investor may request.  Upon the written request
     of an Initial Investor made within 10 days after the receipt of notice from
     the Company (which request shall specify the number of Registrable
     Securities intended to be disposed of by such Initial Investor), the
     Company will use its best efforts to effect the registration under the
     Securities Act of all Registrable Securities that the Company has been so
     requested to register by the Initial Investor, to the extent requisite to
     permit the disposition of the Registrable Securities so to be registered;
     provided, however, that (A) if such registration involves a Public
     Offering, the Initial Investor must sell their Registrable Securities to
     the underwriters selected as provided in Section 3(b) hereof on the same
     terms and conditions as apply to the Company and (B) if, at any time after
     giving written notice of its intention to register any Registrable
     Securities pursuant to this Section 3 and prior to the effective date of
     the registration statement filed in connection with such registration, the
     Company shall determine for any reason not to register such Registrable
     Securities, the Company shall give written notice to the Initial Investor
     and, thereupon, shall be relieved of its obligation to

                                      -5-


     register any Registrable Securities in connection with such registration.
     The Company's obligations under this Section 2(e) shall terminate on the
     date that the registration statement to be filed in accordance with Section
     2(a) is declared effective by the Commission.

     (ii) If a registration pursuant to this Section 2(e) involves a
     Public Offering and the managing underwriter thereof advises the
     Company that, in its view, the number of shares of Common Stock,
     Warrants or other shares of Common Stock that the Company and the
     Initial Investor intend to include in such registration exceeds
     the largest number of shares of Common Stock or Warrants
     (including any other shares of Common Stock or Warrants of the
     Company) that can be sold without having an adverse effect on
     such Public Offering (the "Maximum Offering Size"), the Company
     will include in such registration, only that number of shares of
     Common Stock or Warrants, as applicable, such that the number of
     shares of Registrable Securities registered does not exceed the
     Maximum Offering Size, with the difference between the number of
     shares in the Maximum Offering Size and the number of shares to
     be issued by the Company to be allocated (after including all
     shares to be issued and sold by the Company) among the Company
     and the Initial Investor pro rata on the basis of the relative
     number of shares of Common Stock or Warrants offered for sale
     under such registration by each of the Company and the Initial
     Investor.

          If as a result of the proration provisions of this Section 2(e)(ii),
any Initial Investor is not entitled to include all such Registrable Securities
in such registration, such Initial Investor may elect to withdraw its request to
include any Registrable Securities in such registration.  With respect to
registrations pursuant to this Section 2(e), the number of securities required
to satisfy any underwriters' over-allotment option shall be allocated pro rata
among the Company and the Initial Investor on the basis of the relative number
of shares of Common Stock or Warrants otherwise to be included by each of them
in the registration with respect to which such over-allotment option relates.

          3.   Obligations of the Company

          In connection with the registration of the Registrable Securities, the
Company shall:

          (a)  Promptly (i) prepare and file with the Commission such amendments
(including post-effective amendments) to the Registration Statement and
supplements to the Prospectus as may be necessary to keep the Registration
Statement continuously effective and in compliance with the provisions of the
Securities Act applicable thereto so as to permit the Prospectus forming part
thereof to be current and useable by Investors for resales of the Registrable
Securities for a period of two years from the date on which the Registration
Statement is first declared effective by the Commission (the "Effective Time")
or such shorter period that will terminate when all the Registrable Securities
covered by the Registration Statement have been sold pursuant thereto in
accordance with the plan of distribution provided in the Prospectus, transferred
pursuant to Rule 144 under the Securities Act or otherwise transferred in a
manner that results in the delivery of new securities not subject to transfer
restrictions under the Securities Act (the "Registration Period") and (ii) take
all lawful action such that each of (A) the Registration Statement and any
amendment thereto does not, when it becomes effective, contain an untrue
statement of a material fact or omit to state a material fact required to be
stated therein or necessary

                                      -6-


to make the statements therein, not misleading and (B) the Prospectus forming
part of the Registration Statement, and any amendment or supplement thereto,
does not at any time during the Registration Period include an untrue statement
of a material fact or omit to state a material fact required to be stated
therein or necessary to make the statements therein, in light of the
circumstances under which they were made, not misleading. Notwithstanding the
foregoing provisions of this Section 3(a), the Company may, during the
Registration Period, suspend the use of the Prospectus for a period not to
exceed 60 days (whether or not consecutive) in any 12-month period if the Board
of Directors of the Company determines in good faith that because of valid
business reasons, including pending mergers or other business combination
transactions, the planned acquisition or divestiture of assets, pending material
corporate developments and similar events, it is in the best interests of the
Company to suspend such use, and prior to or contemporaneously with suspending
such use the Company provides the Investors with written notice of such
suspension, which notice need not specify the nature of the event giving rise to
such suspension. At the end of any such suspension period, the Company shall
provide the Investors with written notice of the termination of such suspension;

          (b)  During the Registration Period, comply with the provisions of the
Securities Act with respect to the Registrable Securities of the Company covered
by the Registration Statement until such time as all of such Registrable
Securities have been disposed of in accordance with the intended methods of
disposition by the Investors as set forth in the Prospectus forming part of the
Registration Statement;

          (c)  (i) Prior to the filing with the Commission of any Registration
Statement (including any amendments thereto) and the distribution or delivery of
any Prospectus (including any supplements thereto), provide (A) draft copies
thereof to the Investors and reflect in such documents all such comments as the
Investors (and their counsel) reasonably may propose and (B) to the Investors a
copy of the accountant's consent letter to be included in the filing and (ii)
furnish to each Investor whose Registrable Securities are included in the
Registration Statement and its legal counsel identified to the Company, (A)
promptly after the same is prepared and publicly distributed, filed with the
Commission, or received by the Company, one copy of the Registration Statement,
each Prospectus, and each amendment or supplement thereto, and (B) such number
of copies of the Prospectus and all amendments and supplements thereto and such
other documents, as such Investor may reasonably request in order to facilitate
the disposition of the Registrable Securities owned by such Investor;

          (d)  (i) Register or qualify the Registrable Securities covered by the
Registration Statement under such securities or "blue sky" laws of such
jurisdictions as the Investors who hold a majority-in-interest of the
Registrable Securities being offered reasonably request, (ii) prepare and file
in such jurisdictions such amendments (including post-effective amendments) and
supplements to such registrations and qualifications as may be necessary to
maintain the effectiveness thereof at all times during the Registration Period,
(iii) take all such other lawful actions as may be necessary to maintain such
registrations and qualifications in effect at all times during the Registration
Period, and (iv) take all such other lawful actions reasonably necessary or
advisable to qualify the Registrable Securities for sale in such jurisdictions;
provided, however, that the Company shall not be required in connection
therewith or as a condition thereto to (A) qualify to do business in any
jurisdiction where it would not otherwise be required to qualify but for this
Section 3(d), (B) subject

                                      -7-


itself to general taxation in any such jurisdiction or (C) file a general
consent to service of process in any such jurisdiction;

          (e)  As promptly as practicable after becoming aware of such event,
notify each Investor of the occurrence of any event, as a result of which the
Prospectus included in the Registration Statement, as then in effect, includes
an untrue statement of a material fact or omits to state a material fact
required to be stated therein or necessary to make the statements therein, in
light of the circumstances under which they were made, not misleading, and
promptly prepare an amendment to the Registration Statement and supplement to
the Prospectus to correct such untrue statement or omission, and deliver a
number of copies of such supplement and amendment to each Investor as such
Investor may reasonably request;

          (f)  As promptly as practicable after becoming aware of such event,
notify each Investor who holds Registrable Securities being sold (or, in the
event of an underwritten offering, the managing underwriters) of the issuance by
the Commission of any stop order or other suspension of the effectiveness of the
Registration Statement at the earliest possible time and take all lawful action
to effect the withdrawal, recession or removal of such stop order or other
suspension;

          (g)  Cause all the Registrable Securities covered by the Registration
Statement to be listed on the principal national securities exchange, and
included in an inter-dealer quotation system of a registered national securities
association, on or in which securities of the same class or series issued by the
Company are then listed or included;

          (h)  Maintain a transfer agent and registrar, which may be a single
entity, for the Registrable Securities not later than the effective date of the
Registration Statement;

          (i)  Cooperate with the Investors who hold Registrable Securities
being offered to facilitate the timely preparation and delivery of certificates
for the Registrable Securities to be offered pursuant to the registration
statement and enable such certificates for the Registrable Securities to be in
such denominations or amounts, as the case may be, as the Investors reasonably
may request and registered in such names as the Investor may request; and,
within three business days after a registration statement which includes
Registrable Securities is declared effective by the Commission, deliver and
cause legal counsel selected by the Company to deliver to the transfer agent for
the Registrable Securities (with copies to the Investors whose Registrable
Securities are included in such registration statement) an appropriate
instruction and, to the extent necessary, an opinion of such counsel;

          (j)  Take all such other lawful actions reasonably necessary to
expedite and facilitate the disposition by the Investors of their Registrable
Securities in accordance with the intended methods therefor provided in the
Prospectus which are customary under the circumstances;

          (k)  Make generally available to its security holders as soon as
practicable, but in any event not later than three (3) months after (i) the
effective date (as defined in Rule 158(c) under the Securities Act) of the
Registration Statement, and (ii) the effective date of each post-effective
amendment to the Registration Statement, as the case may be, an earnings
statement of the Company and its subsidiaries complying with Section 11(a) of
the Securities Act and the rules and regulations of the Commission thereunder
(including, at the option of the Company, Rule 158);

                                      -8-


          (1)  In the event of an underwritten offering, promptly include or
incorporate in a Prospectus supplement or post-effective amendment to the
Registration Statement such information as the managers reasonably agree should
be included therein and to which the Company does not reasonably object and make
all required filings of such Prospectus supplement or post-effective amendment
as soon as practicable after it is notified of the matters to be included or
incorporated in such Prospectus supplement or post-effective amendment;

          (m)  (i) Make reasonably available for inspection by Investors, any
underwriter participating in any disposition pursuant to the Registration
Statement, and any attorney, accountant or other agent retained by such
Investors or any such underwriter all relevant financial and other records,
pertinent corporate documents and properties of the Company and its
subsidiaries, and (ii) cause the Company's officers, directors and employees to
supply all information reasonably requested by such Investors or any such
underwriter, attorney, accountant or agent in connection with the Registration
Statement, in each case, as is customary for similar due diligence examinations;
provided, however, that all records, information and documents that are
designated in writing by the Company, in good faith, as confidential,
proprietary or containing any material nonpublic information shall be kept
confidential by such Investors and any such underwriter, attorney, accountant or
agent (pursuant to an appropriate confidentiality agreement in the case of any
such holder or agent), unless such disclosure is made pursuant to judicial
process in a court proceeding (after first giving the Company an opportunity
promptly to seek a protective order or otherwise limit the scope of the
information sought to be disclosed) or is required by law, or such records,
information or documents become available to the public generally or through a
third party not in violation of an accompanying obligation of confidentiality;
and provided, further, that, if the foregoing inspection and information
gathering would otherwise disrupt the Company's conduct of its business, such
inspection and information gathering shall, to the maximum extent possible, be
coordinated on behalf of the Investors and the other parties entitled thereto by
one firm of counsel designed by and on behalf of the majority in interest of
Investors and other parties;

          (n)  In connection with any underwritten offering, make such
representations and warranties to the Investors participating in such
underwritten offering and to the managers, in form, substance and scope as are
customarily made by the Company to underwriters in secondary underwritten
offerings;

          (o)  In connection with any underwritten offering, obtain opinions of
counsel to the Company (which counsel and opinions (in form, scope and
substance) shall be reasonably satisfactory to the managers) addressed to the
underwriters, covering such matters as are customarily covered in opinions
requested in secondary underwritten offerings (it being agreed that the matters
to be covered by such opinions shall include, without limitation, as of the date
of the opinion and as of the Effective Time of the Registration Statement or
most recent post-effective amendment thereto, as the case may be, the absence
from the Registration Statement and the Prospectus, including any documents
incorporated by reference therein, of an untrue statement of a material fact or
the omission of a material fact required to be stated therein or necessary to
make the statements therein (in the case of the Prospectus, in light of the
circumstances under which they were made) not misleading, subject to customary
limitations);

          (p)  In connection with any underwritten offering, obtain "cold
comfort" letters and updates thereof from the independent public accountants of
the Company (and, if necessary,

                                      -9-


from the independent public accountants of any subsidiary of the Company or of
any business acquired by the Company, in each case for which financial
statements and financial data are, or are required to be, included in the
Registration Statement), addressed to each underwriter participating in such
underwritten offering (if such underwriter has provided such letter,
representations or documentation, if any, required for such cold comfort letter
to be so addressed), in customary form and covering matters of the type
customarily covered in "cold comfort" letters in connection with secondary
underwritten offerings;

          (q) In connection with any underwritten offering, deliver such
documents and certificates as may be reasonably required by the managers, if
any; and

          (r) In the event that any broker-dealer registered under the Exchange
Act shall be an "Affiliate" (as defined in Rule 2729(b)(1) of the rules and
regulations of the National Association of Securities Dealers, Inc. (the "NASD
Rules") (or any successor provision thereto)) of the Company or has a "conflict
of interest" (as defined in Rule 2720(b)(7) of the NASD Rules (or any successor
provision thereto)) and such broker-dealer shall underwrite, participate as a
member of an underwriting syndicate or selling group or assist in the
distribution of any Registrable Securities covered by the Registration
Statement, whether as a holder of such Registrable Securities or as an
underwriter, a placement or sales agent or a broker or dealer in respect
thereof, or otherwise, the Company shall assist such broker-dealer in complying
with the requirements of the NASD Rules, including, without limitation, by (A)
engaging a "qualified independent underwriter" (as defined in Rule 2720(b)(15)
of the NASD Rules (or any successor provision thereto)) to participate in the
preparation of the Registration Statement relating to such Registrable
Securities, to exercise usual standards of due diligence in respect thereof and
to recommend the public offering price of such Registrable Securities, (B)
indemnifying such qualified independent underwriter to the extent of the
indemnification of underwriters provided in Section 5 hereof, and (C) providing
such information to such broker-dealer as may be required in order for such
broker-dealer to comply with the requirements of the NASD Rules.

          4.  Obligations of the Investors

          In connection with the registration of the Registrable Securities, the
Investors shall have the following obligations:

          (a) It shall be a condition precedent to the obligations of the
Company to complete the registration pursuant to this Agreement with respect to
the Registrable Securities of a particular Investor that such Investor shall
furnish to the Company such information regarding itself, the Registrable
Securities held by it and the intended method of disposition of the Registrable
Securities held by it as shall be reasonably required to effect the registration
of such Registrable Securities and shall execute such documents in connection
with such registration as the Company may reasonably request.  As least seven
days prior to the first anticipated filing date of the Registration Statement,
the Company shall notify each Investor of the information the Company requires
from each such Investor (the "Requested Information") if such Investor elects to
have any of its Registrable Securities included in the Registration Statement.
If at least two business days prior to the anticipated filing date the Company
has not received the Requested Information from in Investor (a "Non-Responsive
Investor"), then the Company may file the Registration Statement

                                      -10-


without including Registrable Securities of such Non-Responsive Investor and
have no further obligations to the Non-Responsive Investor;

          (b) Each Investor by its acceptance of the Registrable Securities
agrees to cooperate with the Company in connection with the preparation and
filing of the Registration Statement hereunder, unless such Investor has
notified the Company in writing of its election to exclude all of its
Registrable Securities from the Registration Statement; and

          (c) Each Investor agrees that, upon receipt of any notice from the
Company of the occurrence of any event of the kind described in Section 3(e) or
3(f), it shall immediately discontinue its disposition of Registrable Securities
pursuant to the Registration Statement covering such Registrable Securities
until such Investor's receipt of the copies of the supplemented or amended
Prospectus contemplated by Section 3(e) and, if so directed by the Company, such
Investor shall deliver to the Company (at the expense of the Company) or destroy
(and deliver to the Company a certificate of destruction) all copies in such
Investor's possession, of the Prospectus covering such Registrable Securities
current at the time of receipt of such notice.

          5.  Expenses of Registration

          All expenses, other than underwriting discounts and commissions,
incurred in connection with registrations, filings or qualifications pursuant to
Section 3, but including, without limitation, all registration, listing, and
qualifications fees, printing and engraving fees, accounting fees, and the fees
and disbursements of counsel for the Company, and the reasonable fees of one
firm of counsel to the holders of a majority in interest of the Registrable
Securities shall be borne by the Company.

          6.  Indemnification and Contribution

          (a) The Company shall indemnify and hold harmless each Investor and
each underwriter, if any, which facilitates the disposition of Registrable
Securities, and each of their respective officers and directors and each person
who controls such Investor or underwriter within the meaning of Section 15 of
the Securities Act or Section 20 of the Exchange Act (each such person being
sometimes hereinafter referred to as an "Indemnified Person") from and against
any losses, claims, damages or liabilities, joint or several, to which such
Indemnified Person may become subject under the Securities Act or otherwise,
insofar as such losses, claims, damages or liabilities (or actions in respect
thereof) arise out of or are based upon an untrue statement or alleged untrue
statement of a material fact contained in any Registration Statement or an
omission or alleged omission to state therein a material fact required to be
stated therein or necessary to make the statements therein, not misleading, or
arise out of or are based upon an untrue statement or alleged untrue statement
of a material fact contained in any Prospectus or an omission or alleged
omission to state therein a material fact required to be stated therein or
necessary to make the statements therein, in the light of the circumstances
under which they were made, not misleading; and the Company hereby agrees to
reimburse such Indemnified Person for all reasonable legal and other expenses
incurred by them in connection with investigating or defending any such action
or claim as and when such expenses are incurred; provided, however, that the
Company shall not be liable to any such Indemnified Person in any such case to
the extent that any such loss, claim, damage or liability arises out of or is
based upon (i) an untrue statement or alleged untrue statement made in, or an
omission or

                                      -11-


alleged omission from, such Registration Statement or Prospectus in reliance
upon and in conformity with written information furnished to the Company by such
Indemnified Person expressly for use therein or (ii) in the case of the
occurrence of an event of the type specified in Section 3(e), the use by the
Indemnified Person of an outdated or defective Prospectus after the Company has
provided to such Indemnified Person an updated Prospectus correcting the untrue
statement or alleged untrue statement or omission or alleged omission giving
rise to such loss, claim, damage or liability.

          (b) Indemnification by the Investors and Underwriters.  Each Investor
agrees, as a consequence of the inclusion of any of its Registrable Securities
in a Registration Statement, and each underwriter, if any, which facilitates the
disposition of Registrable Securities shall agree, as a consequence of
facilitating such disposition of Registrable Securities, severally and not
jointly, to (i) indemnify and hold harmless the Company, its directors
(including any person who, with his or her consent, is named in the Registration
Statement as a director nominee of the Company), its officers who sign any
Registration Statement and each person, if any, who controls the Company within
the meaning of either Section 15 of the Securities Act or Section 20 of the
Exchange Act, against any losses, claims, damages or liabilities to which the
Company or such other persons may become subject, under the Securities Act or
otherwise, insofar as such losses, claims, damages or liabilities (or actions in
respect thereof) arise out of or are based upon an untrue statement or alleged
untrue statement of a material fact contained in such Registration Statement or
Prospectus or arise out of or are based upon the omission or alleged omission to
state therein a material fact required to be stated therein or necessary to make
the statements therein (in light of the circumstances under which they were
made, in the case of the Prospectus), not misleading, in each case to the
extent, but only to the extent, that such untrue statement or alleged untrue
statement or omission or alleged omission was made in reliance upon and in
conformity with written information furnished to the Company by such holder or
underwriter expressly for use therein; provided, however, that no Investor or
underwriter shall be liable under this Section 6(b) for any amount in excess of
the net proceeds paid to such Investor or underwriter in respect of shares sold
by it, and (ii) reimburse the Company for any legal or other expenses incurred
by the Company in connection with investigating or defending any such action or
claim as such expenses are incurred.

          (c) Notice of Claims, etc.  Promptly after receipt by a party seeking
indemnification pursuant to this Section 6 (an "Indemnified Party") of written
notice of any investigation, claim, proceeding or other action in respect of
which indemnification is being sought (each, a "Claim"), the Indemnified Party
promptly shall notify the party against whom indemnification pursuant to this
Section 6 is being sought (the "Indemnifying Party") of the commencement
thereof; but the omission to so notify the Indemnifying Party shall not relieve
it from any liability that it otherwise may have to the Indemnified Party,
except to the extent that the Indemnifying Party is materially prejudiced and
forfeits substantive rights and defenses by reason of such failure.  In
connection with any Claim as to which both the Indemnifying Party and the
Indemnified Party are parties, the Indemnifying Party shall be entitled to
assume the defense thereof.  Notwithstanding the assumption of the defense of
any Claim by the Indemnifying Party, the Indemnified Party shall have the right
to employ separate legal counsel and to participate in the defense of such
Claim, and the Indemnifying Party shall bear the reasonable fees, out-of-pocket
costs and expenses of such separate legal counsel to the Indemnified Party if
(and only if): (x) the Indemnifying Party shall have agreed to pay such fees,
costs and expenses, (y) the Indemnified Party and the Indemnifying Party shall
reasonably have concluded that representation of the Indemnified Party by the
Indemnifying Party by the same legal counsel would not be appropriate due to
actual or,

                                      -12-


as reasonably determined by legal counsel to the Indemnified Party, potentially
differing interests between such parties in the conduct of the defense of such
Claim, or if there may be legal defenses available to the Indemnified Party that
are in addition to or disparate from those available to the Indemnifying Party,
or (z) the Indemnifying Party shall have failed to employ legal counsel
reasonably satisfactory to the Indemnified Party within a reasonable period of
time after notice of the commencement of such Claim. If the Indemnified Party
employs separate legal counsel in circumstances other than as described in
clauses (x), (y) or (z) above, the fees, costs and expenses of such legal
counsel shall be borne exclusively by the Indemnified Party. Except as provided
above, the Indemnifying Party shall not, in connection with any Claim in the
same jurisdiction, be liable for the fees and expenses of more than one firm of
counsel for the Indemnified Party (together with appropriate local counsel). The
Indemnified Party shall not, without the prior written consent of the
Indemnifying Party (which consent shall not unreasonably be withheld), settle or
compromise any Claim or consent to the entry of any judgment that does not
include an unconditional release of the Indemnifying Party from all liabilities
with respect to such Claim or judgment.

          (d) Contribution.  If the indemnification provided for in this Section
6 is unavailable to or insufficient to hold harmless an Indemnified Person under
subsection (a) or (b) above in respect of any losses, claims, damages or
liabilities (or actions in respect thereof) referred to therein, then each
Indemnifying Party shall contribute to the amount paid or payable by such
Indemnified Party as a result of such losses, claims, damages or liabilities (or
actions in respect thereof) in such proportion as is appropriate to reflect the
relative fault of the Indemnifying Party and the Indemnified Party in connection
with the statements or omissions which resulted in such losses, claims, damages
or liabilities (or actions in respect thereof), as well as any other relevant
equitable considerations.  The relative fault of such Indemnifying Party and
Indemnified Party shall be determined by reference to, among other things,
whether the untrue or alleged untrue statement of a material fact or omission or
alleged omission to state a material fact relates to information supplied by
such Indemnifying Party or by such Indemnified Party, and the parties' relative
intent, knowledge, access to information and opportunity to correct or prevent
such statement or omission.  The parties hereto agree that it would not be just
and equitable if contribution pursuant to this Section 6(d) were determined by
pro rata allocation (even if the Investors or any underwriters were treated as
one entity for such purpose) or by any other method of allocation which does not
take account of the equitable considerations referred to in this Section 6(d).
The amount paid or payable by an Indemnified Party as a result of the losses,
claims, damages or liabilities (or actions in respect thereof) referred to above
shall be deemed to include any legal or other fees or expenses reasonably
incurred by such Indemnified Party in connection with investigating or defending
any such action or claim.  No person guilty of fraudulent misrepresentation
(within the meaning of Section 11(f) of the Securities Act) shall be entitled to
contribution from any person who was not guilty of such fraudulent
misrepresentation.  The obligations of the Investors and any underwriters in
this Section 6(d) to contribute shall be several in proportion to the percentage
of Registrable Securities registered or underwritten, as the case may be, by
them and not joint.

          (e) Notwithstanding any other provision of this Section 6, in no event
shall any (i) Investor be required to undertake liability to any person under
this Section 6 for any amounts in excess of the dollar amount of the proceeds to
be received by such Investor from the sale of such Investor's Registrable
Securities (after deducting any fees, discounts and commissions applicable
thereto) pursuant to any Registration Statement under which such Registrable
Securities are to be registered under the Securities Act and (ii) underwriter be
required to undertake liability to any

                                      -13-


Person hereunder for any amounts in excess of the aggregate discount, commission
or other compensation payable to such underwriter with respect to the
Registrable Securities underwritten by it and distributed pursuant to the
Registration Statement.

          (f) The obligations of the Company under this Section 6 shall be in
addition to any liability which the Company may otherwise have to any
Indemnified Person and the obligations of any Indemnified Person under this
Section 6 shall be in addition to any liability which such Indemnified Person
may otherwise have to the Company.  The remedies provided in this Section 6 are
not exclusive and shall not limit any rights or remedies which may otherwise be
available to an indemnified party at law or in equity.

          7.  Rule 144

          With a view to making available to the Investors the benefits of Rule
144 under the Securities Act or any other similar rule or regulation of the
Commission that may at any time permit the Investors to sell securities of the
Company to the public without registration ("Rule 144"), the Company agrees to
use its best efforts to:

          (a) comply with the provisions of paragraph (c) (1) of Rule 144; and

          (b) file with the Commission in a timely manner all reports and other
documents required to be filed by the Company pursuant to Section 13 or 15(d)
under the Exchange Act; and, if at any time it is not required to file such
reports but in the past had been required to or did file such reports, it will,
upon the request of any Investor, make available other information as required
by, and so long as necessary to permit sales of, its Registrable Securities
pursuant to Rule 144.

          8.  Assignment

          The rights to have the Company register Registrable Securities
pursuant to this Agreement shall be automatically assigned by the Investors to
any permitted transferee of all or any portion of such securities (or all or any
portion of any Preferred Shares or Warrant of the Company which is convertible
into such securities) of Registrable Securities only if:  (a) the Investor
agrees in writing with the transferee or assignee to assign such rights, and a
copy of such agreement is furnished to the Company within a reasonable time
after such assignment, (b) the Company is, within a reasonable time after such
transfer or assignment, furnished with written notice of (i) the name and
address of such transferee or assignee and (ii) the securities with respect to
which such registration rights are being transferred or assigned, (c)
immediately following such transfer or assignment, the securities so transferred
or assigned to the transferee or assignee constitute Restricted Securities, and
(d) at or before the time the Company received the written notice contemplated
by clause (b) of this sentence the transferee or assignee agrees in writing with
the Company to be bound by all of the provisions contained herein.

          9.  Amendment and Waiver

          Any provision of this Agreement may be amended and the observance
thereof may be waived (either generally or in a particular instance and either
retroactively or prospectively), only with the written consent of the Company
and Investors who hold a majority-in-interest of the

                                      -14-


Registrable Securities. Any amendment or waiver effected in accordance with this
Section 9 shall be binding upon each Investor and the Company.

          10. Miscellaneous

          (a) A person or entity shall be deemed to be a holder of Registrable
Securities whenever such person or entity owns of record such Registrable
Securities.  If the Company receives conflicting instructions, notices or
elections from two or more persons or entities with respect to the same
Registrable Securities, the Company shall act upon the basis of instructions,
notice or election received from the registered owner of such Registrable
Securities.

          (b) If, after the date hereof and prior to the Commission declaring
the Registration Statement to be filed pursuant to Section 2(a) effective under
the Securities Act, the Company grants to any Person any registration rights
with respect to any Company securities which are more favorable to such other
Person than those provided in this Agreement, then the Company forthwith shall
grant (by means of an amendment to this Agreement or otherwise) identical
registration rights to all Investors hereunder.

          (c) Except as may be otherwise provided herein, any notice or other
communication or delivery required or permitted hereunder shall be in writing
and shall be delivered personally or sent by certified mail, postage prepaid, or
by a nationally recognized overnight courier service, and shall be deemed given
when so delivered personally or by overnight courier service, or, if mailed,
three days after the date of deposit in the United States mails, as follows:

     (i)  if to the Company, to:

                    Thermatrix Inc.
                    308 North Peters Road, Suite 100
                    Knoxville, TN 37922
                    Attention:  Edward E. Greene
                    (423) 539-9603
                    (423) 539-9643 (Fax)

                    with a copy to:
                    Wilson Sonsini Goodrich & Rosati, PC
                    650 Page Mill Road
                    Palo Alto, CA 94304-1050
                    Attention:  Michael J. Danaher, Esq.
                    (650) 493-9300
                    (650) 493-6811 (Fax)

     (ii) if to the Initial Investor, to:

                                      -15-


                    The Shaar Fund Ltd.,
                    c/o Levinson Capital Management
                    2 World Trade Center, Suite 1820
                    New York, NY  10048
                    Attention:  Samuel Levinson
                    (212) 432-7711
                    (212) 432-7771 (Fax)

                    with a copy to:

                    Cadwalader, Wickersham & Taft
                    100 Maiden Lane
                    New York, NY 10038
                    Attention:  Dennis J. Block, Esq.
                    (212) 504-5555
                    (212) 504-5557 (Fax)

     (iii) if to any other Investor, at such address as such Investor shall have
     provided in writing to the Company.

The Company, the Initial Investor or any Investor may change the foregoing
address by notice given pursuant to this Section 10(c).

           (d) Failure of any party to exercise any right or remedy under this
Agreement or otherwise, or delay by a party in exercising such right or remedy,
shall not operate as a waiver thereof.

           (e) This Agreement shall be governed by and interpreted in accordance
with the laws of the State of New York.  Each of the parties consents to the
jurisdiction of the federal courts whose districts encompass any part of the
City of New York or the state courts of the State of New York sitting in the
City of New York in connection with any dispute arising under this Agreement and
hereby waives, to the maximum extent permitted by law, any objection including
any objection based on forum non conveniens, to the bringing of any such
proceeding in such jurisdictions.

           (f) The remedies provided in this Agreement are cumulative and not
exclusive of any remedies provided by law.  If any term, provision, covenant or
restriction of this Agreement is held by a court of competent jurisdiction to be
invalid, illegal, void or unenforceable, the remainder of the terms, provisions,
covenants and restrictions set forth herein shall remain in full force and
effect and shall in no way be affected, impaired or invalidated, and the parties
hereto shall use their best efforts to find and employ an alternative means to
achieve the same or substantially the same result as that contemplated by such
term, provision, covenant or restriction.  It is hereby stipulated and declared
to be the intention of the parties that they would have executed the remaining
terms, provisions, covenants and restrictions without including any of such that
may be hereafter declared invalid, illegal, void or unenforceable.

           (g) The Company shall not enter into any agreement with respect to
its securities that is inconsistent with the rights granted to the holders of
Registrable Securities in this Agreement or otherwise conflicts with the
provisions hereof. The Company is not currently a party to any

                                      -16-


agreement granting any registration rights with respect to any of its securities
to any person which conflicts with the Company's obligations hereunder or gives
any other party the right to include any securities in any Registration
Statement filed pursuant hereto, except for such rights and conflicts as have
been irrevocably waived. Without limiting the generality of the foregoing,
without the written consent of the holders of a majority in interest of the
Registrable Securities, the Company shall not grant to any person the right to
request it to register any of its securities under the Securities Act unless the
rights so granted are subject in all respect to the prior rights of the holders
of Registrable Securities set forth herein, and are not otherwise in conflict or
inconsistent with the provisions of this Agreement. The restrictions on the
Company's rights to grant registration rights under this paragraph shall
terminate on the date the Registration Statement to be filed pursuant to Section
2(a) is declared effective by the Commission.

           (h) This Agreement, the Securities Purchase Agreement, the Escrow
Instructions, dated as of a date even herewith (the "Escrow Instructions"),
between the Company, the Initial Investor and Cadwalader, Wickersham & Taft, the
Preferred Shares and the Warrants constitute the entire agreement among the
parties hereto with respect to the subject matter hereof.  There are no
restrictions, promises, warranties or undertakings, other than those set forth
or referred to herein.  This Agreement, the Securities Purchase Agreement, the
Escrow Instructions, the Certificate of Designation and the Warrants supersede
all prior agreements and undertakings among the parties hereto with respect to
the subject matter hereof.

           (i) Subject to the requirements of Section 8 hereof, this Agreement
shall inure to the benefit of and be binding upon the successors and assigns of
each of the parties hereto.

           (j) All pronouns and any variations thereof refer to the masculine,
feminine or neuter, singular or plural, as the context may require.

           (k) The headings in this Agreement are for convenience of reference
only and shall not limit or otherwise affect the meaning thereof.

           (1) The Company acknowledges that any failure by the Company to
perform its obligations under Section 3, or any delay in such performance could
result in direct damages to the Investors and the Company agrees that, in
addition to any other liability the Company may have by reason of any such
failure or delay, the Company shall be liable for all direct damages caused by
such failure or delay.

           (m) This Agreement may be executed in two or more counterparts, each
of which shall be deemed an original but all of which shall constitute one and
the same agreement.  A facsimile transmission of this signed Agreement shall be
legal and binding on all parties hereto.

                                      -17-


          In Witness Whereof, the parties have caused this Agreement to be duly
executed and delivered as of the date first above written.

                                 Thermatrix Inc.

                                 By:___________________________________________
                                    Name:
                                    Title:

                                 The Shaar Fund Ltd.

                                 By:___________________________________________
                                    Name:  Samuel Levinson
                                    Title: Managing Director

                                      -18-