When an HVAC system is run on AC the fan starts immediately. On heat it is customary to provide a delay to insure the plenum is preheated before starting the fan to prevent a blast of cold air.
Look on the inside of the service panel cover and you should find your wiring schematic. From the schematic you will be able to tell if you have a delay on start timer or a temperature sensor in the heat plenum.
If it is a sensor in the heat plenum it may have a manual reset button.
If not, the problem is either in the timer or sensor or you may have a second fan relay for heat.