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What is the make and model of your thermostat and the make and model of the furnace in question?
It might be, but the timed delay relay in the furnace can stick and the motor won't shut off either. That would be easy to check if you can get to the relay from the outside.
Easy enough to find out. Those controllers aren't that expensive and if it isn't that you have a good part for a spare IF one does go out. OR hook up a simple heat only mechanical thermostat to the furnace leads and try it and see if it functions properly.
Just checking back in to see if you were able to get this resolved or do you still need some additional input from me here? This part is HTF in some locations, so get back to me if you need help with that.