Ok the probe is reading 82 and you have a set point of 80 and the heat is off. This is correct you are over temp on the probe the power will shut down until the probe drops to 79.9. The thermometer should be close to the probes temp if it is in the same location and is good accuracy. keep in mind most thermometers are +/-2ºF accuracy and the herpstat is +/- 0.9ºF so it is quite possiable that it will not read the same. Some thermometers are rated to +/-2ºC (4ºF) some of the accurites carry this spec it is quite likely that is going to be very different.