This will sound crazy, but kinda sounds like you have a vacuum leak in the climate control system. There should be a check valve to help maintain vacuum when engine vacuum goes to zero. Most cars have a default mode of heat to windshield if system failure (think the feds require it). If you are losing vacuum, climate control doors would get wierd. Temp could get wierd too. I'd hook up a vacuum gauge after the check valve and see what kinds of readings it gives you in various modes.