The fan in question is the "heater blower". All this does is move the air. Usually the blower does not go bad but needs cleaning out from time to time. What usually causes this part to stop working is the blower motor resisister. I have had 3 burn out. They are about $65.
But as I said, this just moves the air. If you have air blowing out the vents this is not the problem....it has nothing to do with the cooling of the air.