The plan is to have a tank of glycol coolant sitting outside (at around -20C to -40C ambient) and mount a radiator outside. I'll use a fish tank pump or similar to circulate the coolant. Put water cooling blocks onto the TECs so the wood stove heats one side to around 100C to 200C, and the cold coolant coming in brings it back down, to hopefully get a temperature difference in the range of 100C (ish).

It's all just an idea right now, first I have to find TECs that are up to the heat directly touching the stove.

You could use the waste heat that goes up the chimney to warm the fluid with something like an automotive intercooler and set the system up backwards, maybe?

Ohhh, I hadn't thought of that idea. Interesting. I will be sure to experiment with that!

If you cool the exhaust gases too much they will condense in the flu, and the condensation is incredibly corrosive. Stoves/furnaces etc. (except for condensing ones) intentionally waste a lot of heat intentionally keeping the exhaust gases hot just to prevent this.

The hot exhaust also helps create airflow that moves the combustion products out of your living space.

It would be neat to recover otherwise totally wasted heat, just be careful.