Maybe I'm missing something here
, but on at least some vehicles, you set the temperature with a knob, lever, or whatever, which controls a valve, usually in the heater hose. This changes the amount of hot water flowing through the heater core. If the valve (or the knob, lever, linkage etc) fails, you may get no heat (if the valve is stuck colsed), or nothing but heat (if the valve is stuck open). Regardless of whether the A/C compressor is engaged or not.
My guess is a failed water control valve. Had it happen on my old pickup.