Edgestar 12,000 portale air conditioner and heater

There are 3 possibilities beginning with the most likely problem

1) If your heater heats up for a few minutes and then quits, chances are there is a blockage in the air flow, check for dust and grime blocking the air intake coarse filter , airgun blow to clear accumulated dust and otherwise clean the coarse filter .
2) If the heater fan blows but there is no warm air, the heating element needs renewal ( this happens very rarely)
3)If the fan stalls and the heater heats up and the thermostat kicks in, then this will be not be a DIY job. This is least likely as you said the air cooler works.