Your heater core is part of your coolant system. I'd reckon it'd get flushed with the rest of it.
But I'm no professional.
When you turn it on, does it actually blow out air? Regardless of temperature - Just making sure it's not the blower motor.
If you turn it on, and you hear a clunk/click, and air DOES come out, the pitch of the clunk/click would determine whether it is an air bubble or some sort of shredded metal.
If it dumped all of it's antifreeze over night, or at a time it was not running and hadn't run recently (not hot) then I'd assume it to be your radiator. I mean, the coolant won't move without the engine running. If the engine wasn't running, it couldn't be your water pump.
I'd recommend you simply go to autozone, and have them Pressure Check your Coolant System. I'm pretty sure they'll do it for free. (Just be courteous and buy your parts from there if you so need them.) Autozone honestly tends to be pretty good with this stuff.
They'll know what kind of pressure you should have vs what you do have. and you can then get under the car and SEE where you're leaking.
If you're car never gets low on antifreeze, it's not a leak. But a piece of metal anywhere isn't going to prevent the coolant from heating up. In fact, even an air bubble couldn't prevent the heat. and eventually, the bubble will move itself to your radiator. Like...That's how you bleed the air form a coolant system.. You run it, add/remove pressure via cap on/off, and it'll fix itself right up. But I just don't understand.
A collapsed hose could be the clunk - The sound you hear could be it shutting when pressure is put on - and you wouldn't really hear the sound when the pressure is removed becasue it's rubber, it get's back to shape slowly.
This liverhuyen2003 guy is pretty fancy, but vehicles aren't so complex that I'm even going to bother reading what he's said. He's said enough that I'm sure he's right.
I'm going to go ahead and submit this though, because it's a simple explanation / theory. with very simple / cheap fixes.
He's said so much that I won't read it but he's also said so much that it sounds expensive. ;)
It's a cooling system. It's like $200 to replace it all. ( Minus man hours.)