Factory Temp Guage not working.

Yes it should. If you have a volt meter you can check that wire for pulsating 2.5 to 3.5 volts through the gauge also. If there is no current either the gauge is loose from the circuit board or its fryed inside.
Check the pins on the back of the circuit board where the wires plug....over the years the solder that holds the pins in place will crack and open the curcuit...it is very hard to see inside the dash...you will have to remove the cluster to get a real good look and repair it if that is the problem