You sure you didn't maybe turn the heater all the way up?

Yes. I checked the functionality of all the climate controls. Fan turns on and speed adjusts correctly when I twist that knob. Each of the vent positions works correctly when I twist that knob. Fresh/Recirc button does the correct thing. And when I twist the hot/cold knob, it does correctly go back and forth between heated air and non-heated air. The only thing is that the non-heated air isn't being cooled (despite the fact that I can hear the compressor engage when I press the AC button).