I just bought a 2005 g35 coupe. The temp gauge worked fine when I was test driving it but now when I drove to work this morning it didn’t move from cold. I drive 10 miles to get to my job. Would this just need a new coolant sensor?

 

Use an OBD2 scanner and check coolant temp, this will tell you what's being reported by the sensor. Typically if the coolant temperature doesn't rise within the specified time you will have a CEL for the thermostat function.

The coolant sensor itself is very easy to troubleshoot, you just need a temperature probe that will go to 200F, or an IR gun in that range, a stovetop, small pan to heat the water, and a digital multimeter to read the resistance values. Tables are listed in the FSM under section EC - Engine Controls, look in the table of contents for the DTC on "thermostat function".

You can also take that IR thermometer and shoot the upper/lower radiator hoses to make sure the thermostat opens and pumps out hot water. If you NEVER see a big spike in temperature your thermostat may be stuck open.

If the OBD2 data is sending the correct temperature but the gauge isn't moving then your instrument cluster probably failed.