there might be another reason for the fan not starting.
Are you shure that the temperature is high enough to switch on the fan?
The Saturno temp gauge is well know for showing much to much
Most of the earlier models did show this.
Later on Luigi added an exta resistor in the wiring loom to keep the needle away from the red line.
Beside this the sensor for the gauge in the cylinder head may show wrong data.
I had this on my Nordie some years ago.
The gauge was always near the red line.
I crossed my fingers taht i did not have a water pump problem.
Later on the needle did not drop down to the when the engine was cold.
I replaced the sensor by someone from a Piaggio scooter and the problem was gone.
The water pump problem occured the next year
ciao Joachim