Heat only blows with throttle

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!

Low coolant, when you rev the engine the coolant flows to the heater core.

Do you have overheating issues? Any noise? Both TSTAT and waterpump may have something to do with it. You'll need to do some figuring out. Unlikely that air will suddenly appear in your system - assuming the system wasn't disturbed. If it came to that low of a coolant level, well where did it go?

You could try getting two birds with one stone... I'd try back flushing your heater core first.. pull the lines off (easy on the cores) and run water through it. You can let some CLR sit in it for a few minutes to loosen up debris, flush it out, bleed your system and see if it worked.

let it run with your cap off, first to try and bleed off the system and to check if you have proper flow at idle. If not, your waterpump could be done for.