an outside idea and probably way off but the Focus, if it is getting too hot runs on 2 cylinders to try and keep the engine cool enough not to damage the headgasket. The temp sensor is in the head near the spark plugs on the 1.8, if it's in the same place on the 1.6 you may be confusing the ECU with some squished wires..... The dash temp gauge is taken from near the thermostat so wouldn't show this issue.

Like I said, could be way off but worth a try