Sounds like the heating elements are over heating and shutting down to me. If the unit goes into heat and the unit cycles or gives you cool air I would suggest that your elements are over heating. The manufacturer I am sure did not design your unit to blow cool air and I'm sure that they designed the elements to stay on while the unit calls for heat. The only reason they would burn up is because there is not enough air to cool them off. Look for a dirty air filter first off, then check to see that all registers are open, make sure there is no blockage on any of the intake or discharge openings. If the unit has been worked on recently, the motor may be the wrong size or the motor may be wired on an incorrect speed. there could be a weak internal limit switch that is automatically resetting. Here is a list of problems that could cause this.
1. Faulty thermostat make sure the thermostat is not affected by a nearby supply air diffuster.
2.Dirty air filter.
3.Dirty evaporator coil
3.Faulty or weak internal limit switch-this would only be true if the switch were auto reset
4 blocked or closed registers
5 blocked cold air return blocked
6.improper fan motor size-horsepower or rpm
7.improper return air duct size
8.improper supply air duct sizes
9.closed manual dampers somewhere in the system