I have a magnetic thermometer that I stick to the lower end of the chimney pipe. (photo is just one similar to what I have)
The "burn-zone" markings on it range from 300 degrees F on the low end to around 575 on the high end.
Temperatures lower than that are marked "Creosote", and higher than 575 is marked "overfire".
If I had a copper coil of water wrapped around the stovepipe, all I would need to do is stoke up the stove a little higher. It is really easy to overfire my stove if I don't watch it.
I stopped by a place today where a guy had a BIG Vermont castings stove. Mine is the smallest model, the Intrepid. My Dad has the medium size, and this guy had the big one. That big one cranked out heat! It has a large flat area on back that a heat exchanger could attach to.