You would need the generator to provide about 100 watts to run the electronics and blower. Something passive like a thermoelectric generator would require a large amount of surface area to get this much power. Something more active like a traditional generator would require significant maintenance. If you’re really concerned your best bet is to get a couple Powerwalls and limit what you run off them. You could go a week running just the furnace and charging cellphones.

Power walls are pretty expensive. Much cheaper-- if you're primary concern is keep heat going and maybe a few other basics-- would be a low-maintenance dual fuel generator. Unlike the powerwall it's run-time isn't limited. Prolonged blackouts will run the powerwall dry, but with a dual fuel generator as long as you can get gasoline or propane you're good to go.

I suppose if you can afford it, go for both and have multiple reduncancy.

Or like a standing bike?

Ride the bike to start the heater in a blackout