To troubleshoot the coolant temperature gauge, check the fuses. If the gauge is not working, disconnect the wire at the Coolant Temperature Sensor and observe the gauge's behavior and if the reading drops, replace the sending unit. If the reading remains high, there may be a short in the wire. If the gauge fails to show any indication once the engine warms up, disconnect the wire at the sending unit and use a jumper wire to connect it to clean ground on the engine. Then, if the gauge still doesn't respond, there may be an open circuit. In order to remove the sending unit, drain the coolant, disconnect the wiring connector, and remove the unit using a wrench. Once you are installing the new unit, tighten it securely without using thread sealer. Finally, connect the wiring connector, refill the cooling system, and check for any coolant leakage or issues with the gauge's function.