Try to find someone with a scanner that will show sensor data. The way you diagnose a failed sensor is to read the sensor data with the engine cold. You compare the intake air temp sensor and the coolant temp sensor. They should be within five degrees of one another. If you don't have the sensor resistance curve for temperature, it's more difficult to say how precisely the sensor is performing as temp rises. You can only see if resistance changes (it will fall) as the coolant temp climbs. You can do this with a simple multimeter.
I don't have a service manual for a Sky but if someone here who does, see if there is a separate sensor for the computer input and one for the gauge. It is this way in some cars. I'd be surprised a failed coolant temp sensor wouldn't set a code since the algorithm to set this code uses time, distance, and sensor reponse to trigger a code. Also, the sensor would still show a reading even if there was no coolant at all since it's a simple thermistor and the hotter it gets, the lower the resistance. It would change it's value slower since air is a poor conductor, but it would still change.
@77 deg F according to the manual the sensor would have 2,796 ohms resistance @ 68 deg F it would have 3,520 ohms resistance. 9 degrees change would be 724 ohms which would be about 80.4 ohms per degree F.
although thr RTD probably isn't perfectly linear and there will be a small difference between any given sensor. that should get you in the ballpark
When a temperature display to reads ---F You generally have either an open RTD or an open wiring circuit . Essentially the display is an ohmmeter calibrated to display it's readings in deg F or deg C according to the resistance characteristics of the RTD it is calibrated to.
Therefore ---F would essentially be infinite resistance. So check your connections and wiring.
I am surprised you are not throwing a code. But I don't see a code in the manual for an erronious water temperature reading.You would think it would at least tell you the car is overheating.
I am not surprised that your fans run all of the time though because the temperature reading is so high that it would cause the controller to switch on all of the cooling fans. or in the case of the LNF run the fan at high speed.
There is only one coolant temperature sensor in the vehicle.
Yes, A dashhawk or similar device that can read live sensor data and error codes would be handy if you know someone that has one..