Temperature gauge not working and check engine light is on.

First check the temperature sending unit(s) to be sure they're plugged in and the terminals aren't spread or corroded. There will be one with two wires, and there may be one with one wire. Next, have the diagnostic fault code(s) read. Many auto parts stores will do that for you for free. Be aware fault codes never say to replace parts or that they're defective. They only indicate the circuit or system that needs further diagnosis, or they state the unacceptable operating condition.