Why would a Pontiac Grand Am GT with a new thermstat have cold air coming out of the defogger and the heater core getting hot?

How do you know the heater core is hot? check the radiator surge tank. I bet its empty. next look down by the thermostat and see if your intake gaskets are leaking coolant. now you are where im at. I just bought a new set of gaskets for my 2002 and am online surching for torque order and values.