To check a thermocouple, disconnect the two leads going to the gauge at the thermocouple. Using a Digital Volt-Ohm Meter (DVOM), set the scale to millivolts and test across the two leads from the thermocouple for voltage when the thermocouple is warm (engine idling at normal temperature). If there is no voltage present, the thermocouple has more than likely failed. If there is voltage, then there may be a problem with the wire connections or the gauge. Thermocouples produce a small electrical charge depending on the heat present at the probe and the gauge measures that voltage.
Bill