As an addition to my first reply.
I would hook up a scanner to the ODII with engine cold and check the coolant temp reading. Then if you can start the engine watch the temp as the engine warms up to see if the ECU is getting a correct reading on coolant temp.
Your temp gauge on the dash can be working fine. but the ECU may not be receiving the signal. So you need to verify that the ECU is seeing what it needs to see.
