Had it been warm/hot it would have confirmed my hunch that the stat hadn’t yet been configured for a heat pump application.
Now depending on the type of stat you bought they may still be true. But we’re at a point that it is a bit harder to figure out whats wrong without specific things to look for; things you’d be unlikely to be able to do.
It’s a Honeywell 5-1-1 programmable thermostat model # RTH2410B. I got a handyman to wire it for me as part of a larger project not related to my HVAC. I wish now I had done it myself. I looked at the wiring and it seems correct but I wish I had taken a look at the wiring in the original thermostat. There is at least one wire that is not connected but, according to the manual, this is not unusual. Unfortunately, since I didn’t dismantle the old stat, I don’t know which wire is disconnected.
Also, nothing in the manual suggests that anything needs to be configured for a heat pump. The only thing I see specifically for an electric heat pump is the jumper for heating fan control.
On Honeywell’s website there is an “quick installation guide” for this particular stat. It can be found right here.
Starting on page 12 (PDF) of the manual there is a configuration process. Item 6 in this process should be set to “1”, “Heat Pump system with auxiliary/ back up heat”
Hallelujah! That’s it! I don’t know how I managed to skip over that page. Thanks a bunch! You just saved me $100 or so for a service technician to come over and think to himself “what an idiot”.