I had the same issue.  There is a valve between the firewall and engine that
allows hot coolant to flow when the heat is on.  When this fails, it's like
turning on the heater, even with the A/C on.  I replaced mine with a part
from the dealer.  Can't remember how much it was, but I do remember it
wasn't much.  Look near the center of the car, you should find it.  Let me
know how you make out.

Best of luck,
Fred

"j.a.s" <j.a.s@verizon.net> wrote in message
news:U09Ag.4576$ee1.1614@trisnddc06...

===============================================
* Reply by Jack D. Russell, Sr. <jackru$$ell2@notmail.com>
* Newsgroup: alt.autos.porsche.944
* Reply to: All; "j.a.s" <j.a.s@verizon.net>
* Date:Thu, 3 Aug 2006 07:32:38 -0400
* Subj: Turn off the heat!
=====================================================

j> '87 944 with climate control
j> The system will switch to full heat with no notice and the AC on.
j> Bad controller?  Where is it located?  Approximate cost and
j> difficulty to install?
j>
j> --
j> Mike
j>

Could be a couple of things. See http://www.tech-session.com/kb/index.php?page=index_v2&id=44&c=4 
. Cheap or free fix. I'd check it first. If not, might be the heater
control valve. See http://www.clarks-garage.com/shop-manual/hvac-01.htm 
. Either way...it could be a lot worse. Good luck.