As noted, the fuel and temp gauge share the same circuit. Usually, when they both stop working, it means that the voltage regulator is bad. It's located on the back of the cluster and is held in place with a small slotted screw. Then, it simply slips out of the printed circuit.
In my experience, the main reason they stop working is due to grounding issues. The ground at the fuel sending unit, is shared by the temp sender. This ground is located in the area below the rear seat (along the face), on the passenger side of the car. The only way to access it is to remove the rear seat, and peel back the carpet until the floor pan is exposed. There, you will see (covered in gorilla snot glue and carpet hair), a single phillips head screw and a terminal mounted to the vertical face of the floor pan. Undo the screw, clean up the terminal, and install a slightly larger sized screw that will cut into fresh metal and get good contact.
I've diagnosed about 1/2 dozen non-working fuel gauges. Only once was it a bad cluster (well, just a bad printed circuit, the gauges all worked fine by themselves). Never was it an issue of a bad voltage regulator. Nearly everytime the gauge didn't work, it was because of bad grounds.
If you do that and the temp gauge still doesn't work, check the wire for cracks. They tend to break from age an heat.