Your motorcycle may have a resistor but not a variable one, mind. What you are describing is a thermistor.
However most automotive applications use a thermistor in which the temperature coefficient is negative with respect to temperature. Resistors, per se, have a positive coeffient wrt temperature. However a thermistor could be referred to as a negative temperature coefficent resistor, but thermistor is so much less of a mouthful.
The simple check is to short the meter-to-thermistor wire to earth - the gauge will peg on full scale. When cold the thermistor will be high reistance and the current through the meter a minimum value.
The voltage regulators for the guage supply are almost bullet proof and they regulate at 10.5 volts, so the meter would still not peg full-scale at cold, even if the full battery voltage was applied - the readings would be wrong, but that is all. Thermistors rarely fail totally.
As to the fallacy that no thermostat always leads to overheating, think upon this. When the thermostat is hot it will open virtually fully so as not to unecessarily impede water flow through the radiator - just as though it was not there...