Yes, the Engine computer does use a several temp sensors depending on the vehicle to optimize performance. There is no guarantee that replacing a sensor will make the truck run better. Sensors do fail, but due to their construction they fail completely, and don't usually go out of range, for example the infamous CPS in 7.3 powerstrokes. ECM's by design check each engine sensor when the vehicle is started and due to the construction of the sensors they tend to fail completely and not just go out of range. Any out of range sensor SHOULD trigger a Check Engine Light on the dash. There's always exceptions to the rule, though.
The temperature sender that your dash gauge uses for signals is not the same sender that your ECM uses to adapt to changes in engine operating conditions. They are separate and not interconnected. If your dash gauge is reading really low despite it being a hot day I would investigate first that the gauge is right (install a new sender) and then look into what is causing the engine to run cold i.e. the thermostat failing in the open position.
