if the temp display in the cockpit is ok then it would not be the temp sender (well not the sensor that is responsible for the temp display). more likely to be the coolant level sensor in the expansion tank. if its electrodes get too dirty it may not sense coolant and this is reported through the same light as over temp.
try cleaning the contacts with an old toothbrush - if that does not work fill slightly over max, that sometimes does the trick. if still no luck replace expansion tank with sensor.