Try connecting an OBD II reader capable of displaying live data, specifically engine coolant temperatures, observing cold engine temperature at ignition on time before starting and/or when idling. Good readers will update coolant temps with some requiring a screen refresh to reflect a different temperature. The reader displays coolant temp signals from the body conrol module. The bcm drives the instrument panel gauges. If a reader displays correct temps then the temperature gauge may be faulty or the electronics in the isntrument panel may be faulty.