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The sensor sits on the valve top. So it is mainly the outside temperature, not the gas temperature...
I think it is more about compensation. If you change from a cool underground car park to hot summer roads the temperature rises and so should the pressure.
If the pressure stays the same but the temperature rises this may be a leakage so the alarm goes off. Thats what seemed to be happening once during testing when I covered the sensor with my (warmer) fingers.
Wow, that looks excellent!
Where do you think they measure the temperature? I wonder how much it actually reflects the gas temperature in the tyre...