fan and radiator have nothing to do with a motor running too cool
that is solely the thermostat's job
first i'd check the accuracy of your gauge using a infrared thermometer on the thermostat neck
you can also check the accuracy of the thermostat by hanging it in water by a thread stuck in the opening part of the thermostat
heat up the water and use a meat thermometer to check the temp when it drops off the thread
or just buy a new thermostat
