[oramit]

It sounds like something is wrong with your installation. That behavior certainly isn't normal for heat pumps and I would get a new vendor. I had a heatpump in my Condo and those things were rock solid, from 20 degrees to 110 I never had issues. In my new house we have a gas furnace and are experiencing the same behavior this winter you describe where the programmed temp and the actual temp in the room wildly diverge.

Just this morning I woke up to it feeling chilly. The thermostat said it was 65 and the programmed temp was 68 but it wasn't running. When the furnace runs it works great but something is off with the controller system. I need to call the heating people....