You could do away with the line voltage t-stat all together. Just buy that $4 solid state relay I linked above I assume you shut the local disconnect off at the condenser outside and turn off the emergency heat(hopefully has a local switch) or independent circuit breaker? You could parallel onto the heat output from your normal t-stat and run it to the 24V relay and use the contact side for 120VAC, and add a 20A light switch to shut off the circulator pump when you're using the heat pump. I can sketch up a diagram if you need some visual guidance
That makes sense. Unfortunately I travel for work somewhat frequently and my wife isn't comfortable messing with the wood burner when I'm not around, so I want to leave the heat pump ready so it's very easily for her to turn it back on at the thermostat. I think I just found what I need, although it's more expensive than that relay. I searched for "hydronic thermostat" instead of line voltage, and it looks like Honeywell makes something that will work for me model TL8100. It should be in Friday so I'll try it out this weekend.
