This question gets asked a lot. The first thing to clarify is - are we talking about reading the surface or probe temps? Single wall pipe gets a surface thermometer, double-wall connector stove pipe gets a probe thermometer. For either pipe you want to avoid continuous, inside the pipe,
temps over 900F. An occasional spike is ok, but you don't want to run it daily up to 1200. OK, then why does the reading differ? Surface temps are going to be cooler than the interior (probe) temps. Single wall pipe will cool down the gases more rapidly so you want to stay for surface temps you want to read about 18" above the stove. The surface readings will be about 30-50% cooler than the actual flue gas temps. That is why the range scales on a stove pipe thermometer start saying "Overfire" or "Too hot" starting around 500F. Try to keep the surface
flue temps between 250 and 400
during the peak of the burn cycle. Once the fire is at the coal only stage it's ok if the temps drift lower. The fire is past the creosote producing stage.
A properly placed and working probe thermometer is going to be more accurate because it's reading the actual flue gas temps. Too hot on a probe thermometer is above 900F. Don't panic if you get a spike above 900F actual (probe) temp when starting up a fire. Probe thermometers react faster because they are in the hot gases. As soon as you start cutting back the air the pipe temperature should start dropping. If you find that you are often spiking above the "Too hot" range, try burning down the coal bed a bit further and closing off the air once the fire is burning strongly, a little sooner. For normal burning, try to keep probe
thermometer temps between 300 and 800
during the peak of the burn cycle.
Regardless of flue temps, remember that this is just a guide. The best instrument is your eyes. Don't be a slave to the thermometer. If the fresh fire is burning strongly, start turning it down, regardless of flue temps, until the fire starts getting lazy. Then let it buildup in intensity again and turn it down again until the flames start getting lazy. Repeat if necessary until the air control is nearly or all the way closed.