It depends some on what kind of heat we are talking. The newer models of propane heaters have electronic ignition-if the flame is blown out it will relight. The standing pilot could blow out but in odd circumstance the burner could try to light until the thermocouple cools-once cool it would shut the gas off. I would caution all with thermostats that are so called mechanical-either bimetal or other mechanical styles. They can bounce while going down the road and cause some awful messes with burners and fans coming on/off with every bump in the road. Ask me how I know. Switch over to digital stat and there should be fewer problems.
2002 Monaco Diplomat 36PBD, Avalanche toad, Glastron MX175 , X5 BMW, Almost enough toys, 3 dogs. 1 longtime wife(48 yrs)