It very likely is a bad temp gauge (bad stepper motor, there's one in each individual gauge). They typically go bad one at a time, over time. Best to replace all 4 fuel, temp, speedo, tach.
Helps to know what year your vehicle is ?? Earlier ones more likely to have problem.
See:https://www.google.com/search?q=200...ome..69i57.17915j0j7&sourceid=chrome&ie=UTF-8
I attempted repairs to mine, gave up...these people will do it for us:
https://circuitboardmedics.com/mustang-instrument-cluster-repair/
Helps to know what year your vehicle is ?? Earlier ones more likely to have problem.
See:https://www.google.com/search?q=200...ome..69i57.17915j0j7&sourceid=chrome&ie=UTF-8
I attempted repairs to mine, gave up...these people will do it for us:
https://circuitboardmedics.com/mustang-instrument-cluster-repair/