Code P0128, possible overheating?

You're looking at a normal condition we never look at. That being what happens after the engine is stopped. During normal operation, the heat is generated "over there" by the cylinders, but the temperature is measured "over here" by the coolant temperature sensor, or in Ford's case, a cylinder head temperature sensor. At the same time, cooled coolant from the radiator is coming back into the engine. The flow keeps carrying heat to the radiator to be dispersed into the air.

When the engine is stopped, that high temperature is still there next to the cylinders, but now there's no cool incoming coolant to carry it away. Within a few minutes that heat spreads out and migrates over to the temperature sensor where it is seen as increasing temperature. That increased temperature due to lack of flow is what you're seeing on the scanner.

As far as suspecting there's something wrong with the sensor, temperature sensors have an extremely low failure rate because there's just one component inside them. That's a temperature-dependent resistor. By far more problems with that circuit are due to corroded or loose terminals in the connector, or occasionally a cut or grounded wire. The one notable exception, since these are so reliable, is Ford had a huge rash of failures in the early '90s. There had to be a manufacturing problem to affect so many of them.

Thank you for your fast reply, It's a relief knowing it's normal and not going to harm my engine.

You're welcome. Please come back to see us with your next conundrum.