i suppose it would be a good idea to check first if the engineis really getting hot or if it's only the gauge
When the needle is in the red area your fan is not running?
That might be a hint to watch the gauge i think.
Maybe it's the sensor.
There are new ones from scooters available.
But ... keep an eye on the water pump.
The fan is switch on by a sensor in the radiator.
When the pump has a problem the water flow to the radiator may be suffering.
So the radiator keeps cool while the engine is overheating and no fan will help
I somewhere have a list of resistance over the temperature.
If you have an Ohm-meter you may check your sensor in the cylinder head first
ciao Joachim
found it....