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.
Actually to a trained eye the ancient analog gauges could
give some early warning to problems.
Car dealers are willing to charge for diagnostic work, even
if they find nothing. However customers don't like to be told
there is nothing wrong. I'm sure it gave unscrupulous car
dealers the opportunity to bill for service that wasn't needed.
I worked for Ford Microelectronics for a few years in the
mid 90's. Even after been pummelled by the Japanese for a couple
of decades the car industry was still driven by one thing: low cost.
I bet the idiot lights were a lot cheaper than the analog gauges.
Low price drives most everything.