overheating when turning off car

74Burntorange said
my 318 did the same, I think its becasue the motor is still hot and so is the coolant, but no flow becasue the motor is off

I think what you are saying is when the car was turned off breifly the temp gauge would race toward hot at switch on. That is one of those bad voltage limiter conditions.
In any situation it's best to check with another mor accurate type gauge.