The temp gauge on your car is connected to the temp sensing thermistor on the engine and has a purple with white tracer stripe. Test as follows:
Remove single purple with white tracer wire from engine temp sensor (thermistor) and connect that wire to ground. This should put the temp gauge at full scale (hot). If it does... then drive around a little and watch the gauge. If it stays solid at hot, then the gauge, power for the gauge, and associated wiring are ok, replace the engine sensor.
If it fluctuates while the wire is grounded... then you have an intermittent somewhere in the wiring from the gauge to the sensor, the gauge could be faulty, or the power to the gauge cluster could be intermittent.