Hi,
If the thermostat is not opening all the way, then the radiator can remain 'cool' and the clutch fan will not heat to the required 155F to cause it to move the fan at engine RPM (making it roar).
I would replace the thermostat first, then the clutch if that did not solve the problem. The thermostat should only cost about $15. The clutch is $100 - $250 item, and will take some 4+ hours to install at home, depending on your skills.
I know someone (highly skilled) who removed the radiator from his 96 Bounder, and had it replaced, then found that the old thermostat did not open all the way. If they lose a tiny amount of wax, it will not fully open. Even new ones can be defective. Get the one for the 1996 F-350 truck with 460" engine.
You will find that many of the F-53 with 460" engine share parts with the F-350 460" truck. Use the 4X4 transmission filter (deeper pan than the 2WD F-350).
Brake pads are shared with the same model year F-450 truck. THey are huge, and last a long time, especially if you lock out overdrive while going down the hills. . .
Fred.