The Monaco's higher up the food change use an adjustable Tstat like
......this for $55. I would use it but you need to set the temp that you want the bay heat on before installing as the degrees may not be marked on the dial. Yes the snap disk would work on 120V as it is nothing but a on/off switch that cannot tell the difference in 12V DC or 120V AC.
By switching to AC you will have to run the generator if driving in below freezing weather. I would test the snap disk by putting it in the freezer to make sure it will close.