One reason why fuel and temperature gauges would stop working on a 1992 Toyota Corolla would be a short in the wires. This would lead to a blown fuse. Check the fuse and replace it.
because it's old, stupid
You need gauges and a refrigerant recovery system.
C. Temperature and Sanitizer Gauges
you don't! remove bezel for gauges, remove four screws for gauge assembly, pull forward and tilt, replace the four bulbs.
you have a shorting wire someplace
Both of those gauges have separate temperature sending units somewhere on the motor block. It is not likely that they would both go out at the same time BUT IT IS POSSIBLE!
If your Chevy trailblazer 2004 gauges are not working, check your fuel pump.
Take it into the shop
The temperature gauges on cars are in Celcius.
Toyota doesnt make a cavalier. The cavalier is made by chevrolet.
Check fuse labeled Gauges.
If the guages then work correctly after the vehicle is started, this is normal.