Whether we are pulling a load or not the truck overheat indicator come on and reflects overheating. When we turn on the heater the temp immediately begins to fall back to normal within a minute or less. The truck also has a periodic whistle noise whether we are driving or sitting still.

First thing I would do is flush the radiator. Turning on the heater is releasing some of the heat in the coolant. To me that means the heat is not being released through the radiator, i.e blocked or restricted radiator.