Use a test light and connect it between the temp sender wire and ground. The test light should glow slightly and the guage should move to full hot. If it does the guage and circuit are working as they are supposed to and you will be needing a temp sender.
If it does not then you will need to do further testing on the circuit.
I was going to look up the wiring diagram for that circuit but for some reason I am unable to at this time. (technical difficulties)
the temp sender has a single wire connector and I believe the wire is yellow with a green tracer.(Might be a blue tracer)