First thing I'd do is ask the ECU what the coolant temp is. A bluetooth ELM3237 OBD2 dongle will give you the connection to the ECU, and an Android app like "Torque" will get you the data.
If the ECU does NOT have the data, I'd suspect either a wiring loom fault (eg broken wire - sometimes hard to find) or a poor earth on the radiator/ECU/battery.
If the ECU does have the data, then it's just an instrumentation issue. Is the needle broken? Is the cabling intact behind the instrument cluster? Has someone changed the stereo unit recently and mucked up the ground wire (add another ground from stereo to dash mount bolt, often fixes instrumentation issues because instruments share that ground).