Well, firts off, the sensor that got relocated wasn't the engine temp sensor. It was the intake air temp sensor. It tells the computer what the temp is of the air that is going to pass over the mass air flow meter. Helps to determine the air density.

Second, the grounding issue can cause gauge fluctuations, but it isn't usually confined to one gauge, as the ecu grounds are also affected. But, that might also explain the poor fuel economy as the computer's ground and the sensor's ground could be different.

I'd have them check it out, as it's a viable concern. Rather pay the checkout than guess from the internet on possible scenarios. Not a harsh, just a thought.