Would the heater core (2000 Lincoln Navigator) be covered by a powertrain warranty?

No... the heater core is not part of your powertrain.

It could depend on what sort of warranty you have. Is it an extended warranty? A powertrain warranty "deluxe" ?

It's more dependent upon who is providing the warranty, the conditions for which the part in question needs to be replaced / repaired and so on.

It's not always all in the fine print, but that's a good place to start. The automobile industry isn't exactly known for integrity and being upfront.

Anyone who says otherwise is tryin to sell ya something. ;)

Technically not, though some *may* regard it as part of the engine cooling system.

It really boils down to semantics, but given that a bad heater core has a pretty direct effect on the radiator (and thus the engine), the argument could be made.

Remember, the Lancer Evolution was originally not allowed to be imported into the US in part because the intercooler for the turbo (an engine component, at least legally) was outside the frame of the vehicle.

no

Only if it's a steam engine.

I don't know. I think tarp might be better, though.