It's the thermostat. It has to get replaced, and the stupid HVAC system installed in the house apparently is not compatible with anything other than a "smart" thermostat, which is not cheap.
Ticks me off because I don't use any of the "smart" features - never hook the dumb thing up to wifi even. I just use it like a regular thermostat. But I get hosed, anyway.
Blah.