The stat isn't really programed to lie.
They tend to read slow, and some round to the next temp too quick.
Do you know the reason why the auto industry switched to idiot lights instead of guages at one time.
Too many people complained that the oil prssure was to high one time and too low the next. Or teh alternator was putting out steady voltage.
Or the engine temp was alittle closer to the next line up, then it was yesterday. Etc.
Which created too many hours of checking for non existant problems. That the dealers couldn't charge for.
If digital stats, responded as fast to temp changes as they could. 99% of the customers would be complaining all the time.