Dallas, have a look at the thermostat on the Wonderwood / Wondercoal cabinet style circulator stoves. They are very similar to some that Ashley sells (or used to), also have seen them under the Suburban brand. They are double-walled stoves with an inner firebox of sheet steel, surrounded by a metal cabinet that stands off about three inches from the firebox all around and on top. The top of the cabinet is a grate that allow passage of lots of air, and the cabinet sides are open at the bottom. The whole space between firebox and cabinet creates an excellent chimney effect and the hot air pours out the top and circulates through the room.
The thermostat on my Wonderwood (1980's vintage) worked extremely well. A bi-metal coil mounts very close to the firebox side, near the top, with a light-weight steel cable running vertically down to a flapper door that covers the air intake. The flapper is hinged at the top, so as the bi-metal coil unwinds, the door lifts open to admit more air, and as the coil winds tighter the door closes. There are two round holes in the flapper door, and a minimum draft opening is maintained by a sliding shutter that is manually adjusted by trial and error to block more or less of the holes. Angles and leverage between the spring and flapper door were such, that the flapper even acted somewhat like a barometric damper, in that when it was almost closed it could be sucked the rest of the way closed by wind-induced draft thereby decreasing the effect of the excess draft. Of course you wouldn't need that feature if you believed in baros (dig, dig -- aren't you the MPD guy?).
Here's a link to the Wondercoal parts list. I wouldn't be surprised if you could just get the parts new from U.S. Stove, or off an old stove if you can find one, and adapt them directly to your stove. Other than getting everything to fit, I would think the biggest issue would be exactly how close to the stove body to mount the bimetal spring, whether to encase it so as to reduce outside air from affecting it, so as to keep it within its designed operating range of temperatures.
This link is broken, either the page no longer exists or there is some other issue like a typo.