If I understand correctly what you are saying I believe you are mistaken about the heater thermostat. When the furnace reaches the set temperature it shuts off the propane from burning that creates heat but the fan continues to run for a time then fan too will turn off. When the temperature drops below the thermostat setting it turns the propane back on to burn and create heat and fan starts at the same time and begins the cycle again. The fan will run for sometime before it turns off I guess this is to keep furnace from overheating or better efficiency off heat. I hope I have this correct maybe someone else may be able to explain it better.
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