[mx6rrr]

Hey everyone!
The cars an 05 ford 500...I fixed the "only blows on speeds 3 and 4" with a new blower resistor but the other problem makes me curious...the car blows heat but only when you press gas peddle, let off and cool air, press gas and warm again!? I'm guessing air in coolant lines or clogged heater core but wondering if that sounds right?
Best way to check heater core is with a temp gun on the lines correct? And I was wondering if this would have anything to do with the thermostat or water pump?
I did try burping the system but it doesn't have a standard radiator cap just the full tank so I'm not sure I did that propperly....
Thanks for any input again guys!