you are making think about something I have not thought about in a while. this hurts.
I assume you have the auto heat.
you have 2 fuses. one for L and M and another for hi. you also have a relay for hi.
relays don't usually stick. the hi spd relay is under the passengers foot board. try removing it If the fans are on HI.
if the fans are on low then the main sw in the controls is bad. in the link it would be the top one in the diagram. this is the one that goes bad and runs the fans all the time, although not sure how it runs the fans with the key off. even with the heat on and key off the fans should not run.
sounds like you may have the power to the heat controls wired to something that has power all the time. I would suspect at the fuse block.
http://forums.pelicanparts.com/911-930-turbo-super-charging-forum/941050-auto-heat-foot-well-blowers-part-deux.html
is this car new to you?
if not have you recently done some wiring work?
I will have to think about the heat controls some more.