The trouble code P0128

Actually, there are two coolant temperature sensors. One is for the gauge and the other tells the ECM [computer] what the coolant temperature is. If your gauge is reading normal, that sensor is probably OK. It is likely the other sensor is giving false info to the ECM which is turning on the light and showing a code P0128. If it is sending a reading that is too low, the ECM demands more fuel from the injectors [usually resulting in poor fuel mileage]. If it is sending a reading that is too high [overheating] the ECM says to lean out the fuel mixture. The vehicle would then be very difficult to start and drive when cold until completely warmed up. False readings somewhere in the middle will give combinations of both symptoms.

Good answer, interesting point. I'd just add that the basic meaning for a P0128 code is:

Coolant Thermostat Problem. Usually not getting hot enough in the time given, that is standard.