Fan clutches only care about the temperature behind the radiator. I have had them at full lockup, screaming, in 30 degree F freezing weather. Depends on the cooling needs.
Is the noise the same "morning sickness" roar you get when you take off after starting the truck? The fan clutch tends to be locked in and kick out in ~2 Min of driving sometimes. This is by design and called morning sickness.
So your fan clutch could be working ok and kicking on due to a restricted radiator, heavy load, engine problems, slipping transmission, dragging brakes, etc. The clutch could be failing, and to test it: Stop and rev the engine to 2K for 2 min. If the clutch does not kick out by 2 min the bearings are locking up and clutch has failed. (Unless things are really hot and the fan needs to run. In case the fan explodes do not rev with the hood up.)
After running the engine or reving for 2 min shut off the engine - assuming the noise quit. The fan should spin by hand 1/2 or more revolutions when completely kicked out. Possible if the fan is hot that it is kicking in to cool things down and not spin much.