you should check your gauge against the scan value for the temperature. It's very possible that the stepper motor for your temp gauge has gone out. The instrument cluster sees that the gauge is reading something noteworthy and turns on the gauges light.
See if you have a code for temperature. Maybe the gauge is correct and the computer agrees. If you have a coolant temp of -40F on the scanner you have an open in you CTS circuit. If your PCM reads a normal temperature reading of 190-210 and the gauge says on the bottom cold, probably the gauge stepper.
A lot of the clusters now do not have removable light bulbs and gauges. they are all soldered into the circuit board. If you are good with that sort of stuff you can unsolder and remove, then replace the parts and solder back into the printed circuit board. If not then you have to replace the cluster.