The temperature gauge is completely separate to the thermostat and cooling system control, what you see on the gauge in front of you is just a reading from it’s own brass sender, 99.9% it’s nothing to worry about, everything will be normal but the sender is giving a false reading.

Either the sender is bad, the wiring, or the actual gauge is broken, again 99.9% of the time it’s the wiring or the sender so very cheap fix.