Better Thermostat

Sure, any thermostat that provides a contact closure when calling for heat will work. If you get an electronic one then it needs to operate on 12Vdc. I use on of these little W1209 tstats to better control the water heater. The W1209s are incredibly cheap yet very versatile and run on 12V. If you don’t want it visible on the wall you can put it somewhere concealed and just locate the thermistor temp sensor where it gets a good interior temp, away from the furnace vent of course. You can also calibrate it with an accurate thermometer.


Tstat

As for the furnace tolerating it that’s a good question. You don’t want it to short cycle too much so the temp delta (aka hysteresis) of the tstat can’t be too tight.. But the furnace has a built in time delay as the fan runs for awhile after the gas shuts off. The W1209’s have settable hysteresis and time delay so you can play with it if you think it’s short cycling too much.

To paraphrase Forrest Gump, pretty is as pretty does.

You're correct. It was on d2. I just put it on d1. We'll see how it does tonight.