Though with a generator that big and some ingenuity you can plumb the radiator into the house and get heat from the engine. The more load on the genererator the more heat.

Schemes like that are generally how CO poisoning stories start. Or fires. A door gets cracked to run a hose through... etc.

Besides, at some point, you're just reinvinting an overly complicated combustion heater.

Which I already have, is already hardwired for fuel, and only needs to be plugged in.

Very much true. I didn't touch on safety which is a real issue.

That doesn't make the idea bad though. There have been attempts to do this in commercial furnaces before, but the details are hard, and ultimately of questionable value in general. In this particular situation it might be useful, but that is a lot of complexity for something that only makes sense for a week every 10 years.

Maybe not a heating element, but heat punp?

It's more an explanation of how you can have gas heat without power. Also, even heat pumps use a heating element at some point below 28~30 degrees. If you rely on the pump only below that, it'll start to freeze up into an ice block itself at some point.

Plus having a continuous plug-in (natural gas) fuel source is a big advantage over refilling a gasoline generator, which most portable generators are.

Heat pump efficiency drops a lot when the temperature goes significantly below zero celsius