My truck is non A/C model.
My heater door is very easy to activate and doesnt make a sound when done with the switch (control panel, by cable system, no vacuum). If you grab the little lever that the cable attaches to (NOT at the control panel) and shift it real hard (kind of fast and jerky
) then you should hear the slight thunk. I believe there is a small peice of foam glued on from the factory that helps seal and allows a quit shutting of the door. I would check that way before taking it apart and checking it out. I would suspect that your thermostat is ok, but a higher opening temp. would increase your cab heating.