I have a Heil high efficiency furnace about 15 years old. Sometimes the burner will start and the exhaust blower then the blower fan will blow for a short time and stop. The burner will still be very hot. It used to continue to run until the furnace cooled down. What could be wrong?

Could be the blower fan or limit control out of calibration causing the blower to stop short of removing all the heat from the unit or the blower motor could also be getting hot and shutting down.

What to do is fix it. Check the controls mentioned and replace he defective one. I cannot do that for you because I live to far away. LOL