joeq wrote:My Surdiac has a heat exchanger on the back, and appears to be the only place to put a thermometer.
That's a reasonable place to put it. You're right that you would not want to place it on the outer shell.
Most folks use a magnetic stick-on thermometer somewhere on the stove body, and another one on the stove pipe. Some spots on the stove are hotter than other spots, but just pick a spot where it is easy to see. The particular temperature is not that important, just useful to compare one time to the next. For example, from experience I know that on a typical winter night 450 degrees is about right for my house, or 650 degrees if it's going to be REALLY cold. If I moved the thermometer to a cooler or hotter spot on the stove, I'd have to start learning all over again.
A probe thermometer can be used on the stovepipe, but IMHO it is overkill. A magnetic one can be easily moved around to different pipe locations, or moved to the stove itself. My rule of thumb is, the gas temperature as measured by a probe will be about 1.8 times the surface temperature shown by the magnetic. And as long as the chimney is drafting properly, the stove is burning well, and flue temperature is not excessively low or high, that's close enough.