Temperature gauge

There are likely two coolant temperature sensors. The two-wire sensor is for the Engine Computer. When there is a second sensor for the dash gauge, it will have just one wire. Unplug that one-wire sensor, then see what the gauge does. If it stays on "hot", turn the ignition switch off, then measure the resistance on that wire to a paint-free point on the engine block. If you find low resistance, probably in the area of 100 ohms or less, that wire is grounded somewhere. If there is no short on that wire, suspect a problem on the instrument cluster.

On newer cars there is often just one coolant temperature sensor. It will have two wires and feeds the Engine Computer. That computer sends data to the instrument cluster. For that circuit, you need a scanner to view live data to see the temperature the Engine Computer is seeing. If it is normal, the instrument cluster is most likely receiving the right data but it is interpreting it wrong.

Coolant temperature sensors are usually on or near the thermostat housing.