Fuel injected engines have 2 coolant temp units on the engine
ECT sensor, 2 wire, 5volts, only used by the engine computer
Coolant temp sender, 1 or 2 wires, 12volt, only used by dash board temp gauge
Sender will have a red/white wire that runs to the cluster, and it can have a black/white ground wire or just the one red/white wire and is grounded via its threads to the engine metal
Find it and unplug it
Turn on the key, temp gauge should stay at COLD
Turn off the key
Ground the red/white wire to battery negative or metal on engine, with a jumper wire
Turn on the key, temp gauge should go to HOT
If this happens then replace sender the wiring and gauge are OK
(make sure you get a Temp SENDER, people are often sold an ECT sensor by mistake, one is 5v the other 12v so NOT interchangeable)
If temp gauge goes to 1/2 with key on when sender is unplugged then its an issue with wiring or gauge