I do own a much older generation Thermapen - the automatic switch is failing, so I need to open it up and fix it... but I do find it a useful tool.
For the HN angle, my understanding on how these devices get such a fast reading is to have a decent calibration of the thermal mass of the probe tip, some reasonably quick and precisely timed readings and then using some math to interpolate the exponential curve to predict what the probe temperature is. After a few seconds thermal equilibrium is reached, but it is likely you've already been looking at something close to the final value.
[edit] after doodling on paper, not sure it is necessary to know the thermal mass of the probe. Time to do some experiments!
If you don't want to fix it yourself Thermoworks will repair it for next to nothing. I think I paid like $10 to have one with a similar issue fixed. Normally it is something with the case around the pivot point that causes it to stop turning on (try squeezing it in that area to test that theory).
The speed compared to most other thermometers is that that is uses a thermocouple vs a thermistor. The cheaper ThermoPop uses a thermistor and takes about twice as long to get a reading.
For the HN angle, my understanding on how these devices get such a fast reading is to have a decent calibration of the thermal mass of the probe tip, some reasonably quick and precisely timed readings and then using some math to interpolate the exponential curve to predict what the probe temperature is. After a few seconds thermal equilibrium is reached, but it is likely you've already been looking at something close to the final value.
[edit] after doodling on paper, not sure it is necessary to know the thermal mass of the probe. Time to do some experiments!