I believe that blue-bodied temperature switch also gives input to the climate control system. With it unplugged you might have some wacky operation from the system - such as no heat.

Is your problem that the fans are coming on at too high of an engine temperature? If the temperature switch is still funtioning you can try installing a resistor across the leads to lower the temperature at which the high aux fans turn on. I installed a variable resistor inside the car to determine what value the resistor needed to be. 2K ohms seems to be what I need but that will probably vary for your car.