The fan is controlled by your engine control module. The coolant temperature is reported to the engine control module by the coolant temperature sensor in the thermostat housing.
Before jumping into further repairs, you should make an audit of your cooling system's performance.
First, check your coolant level. If low, check for and repair any leaks.
Next, check for proper coolant flow. With the engine cold, remove the radiator cap and start the engine (a/c off). You should see the coolant circulate through the radiator prior to the fan turning on and prior to coolant boiling out of the radiator. If not, you have something preventing flow. In most cases, this is caused by a stuck thermostat, but can also be caused by a clogged radiator. If you have trouble seeing well enough into the radiator to tell whether you have coolant flow, you can feel the hoses. If only one hose is hot, the coolant is not flowing. If both hoses are hat, the coolant is flowing.
Once you've determined you have coolant flow, allow the engine to continue to run. The radiator fan should begin to cycle on and off as necessary to manage coolant temperature. It should continue doing this without the coolant boiling out of the radiator.