It sounds like the engine driven fan is functioning properly. At about 100C the clutch should tighten and it will "roar" at about 2000 revs, but it cannot move enough air at idle speed.
Your electric fan(s) should engage high speed at about 105C and you should be able to hear it. You can run a test by idling the car with the hood open and observing electric fan operation. (Keep the A/C off.) If it does not engage high speed by about 110C then it's likely there's a problem either with the fan motor or the fan control circuit.