I don't think you know what a thermostat is or what it does. It does not "read" anything. It is a mechanical valve that opens and closes at a certain temp. When the thermostat is closed, the coolant circulates within the engine and bypasses the rad. When it reaches a certain temperature, the thermostat will open and the coolant will flow through the rad. A faulty thermostat will open too early, or stick open at all times. This will cause overcooling as you described.
Also the cold start function will not make the fuel pump pump extra fuel, it will tell the injectors to pulse for longer, allowing more fuel in. The fuel pump is on all the time. whatever is not sprayed through the injectors is sent back to the fuel tank and pumped again until it is finally used.
Also the cold start function will not make the fuel pump pump extra fuel, it will tell the injectors to pulse for longer, allowing more fuel in. The fuel pump is on all the time. whatever is not sprayed through the injectors is sent back to the fuel tank and pumped again until it is finally used.