Does the system change modes, meaning when you hit specific push-buttons, does air come out of the appropriate vents (windshield, side dashboard vents, below dashboard, dashboard center air vents (cold air only)?
It could be that the interior air sampler fan is not working, which gives an incorrect reading to the pushbutton unit and makes it think there is another temperature inside the car. The air sampler fan is located behind the airbag on the passenger side, behind the air vent on that side of the dash. There is a thread about finding and replacing it.
The fan pulls air down from the small grill on the sunroof/interior light control panel overhead, via a rubber tube that runs down the passenger side "A" pillar and to the sampler fan. You can check the operation of this fan motor by placing a small piece (the size of a thumb nail) of light, tissue type paper (something like a cigarette rolling paper or a piece of Saran wrap is perfect) against this grill, with the climate control system on. If the fan is working, it will hold the piece of paper against the grill. If the fan is not working, it will fall into your lap/to the floor.
Again I think this process is found within threads here on the forum.
It is possible that the push-button unit is worn out, as well, but check the air sampler fan/motor operation first.
The factory service manual also has a procedure for testing the operation of the system.