the thermostat is nothing more than a metal casing holding a wax pellet against a diaphragm. As the engine heat increases the coolant makes the wax expand forcing open the diaphragm allowing the coolant to pass into the radiator to cool down before recirculating to the engine to cool said engine. If the thermostat is stuck closed then no coolant flows and stagnates within the block not removing heat. Your CTS coolant temp sensor is what governs some engine/trans functions via ECU/PCM/whatever it's called today and that light coming on and off.