I had a similiar heat problem with my 97 Mark VIII. From my research I found that a common problem is that the Blend Door actuator motor goes out or the control arm attached to the motor breaks. If you can find the right codes and which buttons to push, the car should tell you if the motor is bad.
Along with the motor, and finding some parts that were missing, I also had to replace the control unit. Good luck and I hope his helps