The unit turns on when thermostat temperature is set higher than room temp. It blows cool air for several minutes and then the emergency heat kicks on and warmer air comes from vent. This lasts for several minutes then shuts off, air continues to blow but is now cool again. At this point room temperature never reaches the set point the unit continues to run continually until it is shut off at the thermostat.
In the heat mode the larger copper pipe going to the AC unit outdoors should get very hot, if not then the refrigerant might be low or the reversing valve which switches modes from Cool to Heat may be bypassing. the fact it shuts down tells me its getting overheated likely due to low refrigerant level.