Reddit reviews VODA 4-Blade Heat Powered Stove Fan for Wood/Log Burner/Fireplace Increases 80% More Warm air Than 2 Blade Fan- Eco Friendly

How about something like this?

4-Blade Heat Powered Stove Fan

Looks like that's peltier-powered, not a stirling engine, but it might get the job done.

DIY version

If you're really set on stirling engines this site may help. What you propose is certainly possible, but it'd be a big job and even then I'm not sure you'd get enough power to match your bellows.

That is a really good idea. Were you referring to something like this:

https://www.amazon.com/VODA-4-Blade-Fireplace-Increases-Friendly/dp/B01CD2AIV8/ref=sr_1_3?keywords=oven+convection+fan&qid=1570733996&sr=8-3

I got this one a few years ago. It's more of a novelty than anything else. It spins its little ass off when the stove is going, but I cant really feel any air moving from it. When it dies, I won't replace it.

They run off piezo electric current Peltier Generator wherein the heat source needs to get hot enough to stress the materials which create the electricity required for operation (https://en.wikipedia.org/wiki/Piezoelectricity) (https://en.wikipedia.org/wiki/Thermoelectric_generator). There are wires that run from the solid material layer into the fan engine to power it, which then runs until the heat source cools down and it automatically shuts off (due to lack of heat power). The fans are relatively cheap too, I got mine on Amazon for like $40 and it works great and looks good as well. The main benefit is that they push the hot air off the top of the hear source (hot air rises) so instead of that air immediately going up to the ceiling it goes out in the room first before rising eventually. Mine usually kicks on when the surface it's touching reaches about 200 degrees and will run continually for as long as I keep my stove above that temperature. In case you want one, here's the one I bought off Amazon (https://www.amazon.com/gp/product/B01CD2AIV8/)