Usually when we camp, we just use our furnace to warm up in the morning, then shut it off after getting out of bed. When we were up in the mountains of Nevada, and it was really chilly, we let the furnace run for quite some time, and I was surprised at how often the furnace would cycle on and off.
You need to cut the connectors off the wires to the existing thermostat in order to remove the existing thermostat and mount the new one - make sure your house battery is disconnected!
Slide the wires through the backing plate of the new thermostat, crimp on some new connectors, screw them down, reconnect your house battery and try it out!
I ended up with the top screw hole from the old thermostat showing - you can barely see it. The off/on temperature control is on the top, not the bottom, but I think I can live with that - I like the look of the old thermostat better, but I think I can live with that, too.
BIG DIFFERENCE! Now the furnace does not cycle nearly as often. Easy swap out, sub $20 part at PDX RV LLC.