Temperature Problems

What is your question?

Does anybody else have problems with the air in their lude? My ac does not work in the first place but that doesn't bother me as much as the fact that just vent air is heated more than outside air. And now it's winter. On cold nights the car has a hard time keeping the cab warm enough for comfort. The engine heats up great so I know it is not the thermostat. I would am wondering if this a common problem. I'm thinking of changing the heater core.