Hey Joe - Have you ever looked at the
Buddy Heaters? Two of those can really put out some heat. You can set those on Low and let them burn until they run out, which is usually most of the night. And then your furnace thermostat can kick on like you said.
I think the fuel for those is about $7 for a two-pack, which is totally worth it when you're cold.
The only downside is that they have an exposed flame. Our dumb old dog (bless her heart) caught her tail on fire one night. That was an attention getter. She wasn't hurt, but boy did it stink in there.
Anyway, I like your thought process. Either a small portable gen or some space heaters should do the trick. It's too bad that you have to manually switch the plug on the WW. That bit me a couple of times when I forgot to plug the cord back in and the generator was just burning fuel and not charging anything.