The temp gauges on our cars are a joke, just a little better than our oil gauge.
The sensor for the gauge and the sensor for the fan are different. We really need to know what the degree of temperture it is. Maybe adding an aftermarket gauge would be the answer.
We have a laser thermometer that we can point at anything and get a digital readout.
I think that as long as your fan is coming on, you don't have a problem. Does it go on when you turn the defroster on? Whenever Iwant my fan to go on, I just turn the defroster on. Good luck