When it goes to full hot, is it also switching to air out the defrost vents? Defrost, max heat, is the default when the pushbutton c/c unit fails. That's what my car did when I got it. I replaced the whole pushbutton unit with a rebuilt - about $200, I think (ouch) but it fixed the problem. Not sure issues are related but make sure the auxilary water pump is working (key on, engine off, heat on, pump should run). When these fail I believe they can fry the ciruit board on the pushbutton control unit. Circuit board in mine was visibly fried. After reading about the aux water pump I put a 1.5a fuse in the line for the aux pump just in case.

Good luck! Hey, at least you know you've got heat...