It could be a number of things....if I were troubleshooting it I would un-wire the thermostat and separate the wires so they aren't touching each other. I would then short out the heat wire so the unit fires off in heat, let it run for a bit then un-wire it and see if the fan stays running. I would do this several times and this will either tell you it's the thermostat or something else.
Most fossil fuel units the fan is controlled through the heat board in the furnace (I'm assuming your heat is a fossil fuel). The board in the furnace will delay the fan from coming on so the heat exchanger heats up before the fan starts running and the board will delay the fan shutting down to pull the majority of the heat off of the heat exchanger once it cycles off. It COULD be the board in the furnace but I suspect it's the thermostat.
Hopefully your guy isn't what we call a parts changer that can't figure it out and resorts to replacing parts and hoping for the best. With some knowledge, patience and being thorough he can figure it out without costing you a bunch of new un-necessary parts.
How old is the unit by the way and what type of heat do you have?
Most fossil fuel units the fan is controlled through the heat board in the furnace (I'm assuming your heat is a fossil fuel). The board in the furnace will delay the fan from coming on so the heat exchanger heats up before the fan starts running and the board will delay the fan shutting down to pull the majority of the heat off of the heat exchanger once it cycles off. It COULD be the board in the furnace but I suspect it's the thermostat.
Hopefully your guy isn't what we call a parts changer that can't figure it out and resorts to replacing parts and hoping for the best. With some knowledge, patience and being thorough he can figure it out without costing you a bunch of new un-necessary parts.
How old is the unit by the way and what type of heat do you have?