* Gas gauge: This is part of the fuel system. It measures the level of fuel in the tank using a float sensor and displays the information on the instrument cluster. Problems with the gas gauge can stem from a faulty sending unit (the float), wiring issues, or a problem with the gauge cluster itself.
* Thermostat: This is part of the cooling system. It regulates the engine temperature by controlling the flow of coolant. A malfunctioning thermostat can cause the engine to overheat or run too cold.
While both are important for the vehicle's proper operation, they function independently and a problem with one will not typically affect the other. If you're having issues with both, it's likely two unrelated problems.