My Ford F350 overheats on every hill when I have my cabover camper on and pull my 2 horse trailer. Even without the horse trailer! This is a diesel and should haul a house! I am retired and broke. Wanted to travel during the summer with my horse while I can. So sad.
If the cooling system is full and in reasonable condition take the truck for a drive, when the engine gets above normal operating temperature stop and check if the radiator cooling fan has engaged. It will always be turning but it should be moving a great amount of air when engaged. Have an assistant increase the engine speed to 1500 RPMs, the fan should really roar at this speed. If the cooling fan is not working properly the clutch may have failed or the wires to the clutch may be broken.
If the fan is working consider a failing thermostat, I have seen cases with thermostats would not fully open on other diesel engines.