First. When towing, use 89 octane. Especially in the heat. In the cool, the air is more apt to help create some power and in the heat the air is apt to hinder power. If that makes sense. (I sure wish sometimes we had a clubhouse to meet in to discuss topics...much easier to get a point across) I see there is a thread now saying 93 is helping some...not sure about that...but may be worth a try sometime.
Do you have a large grade near you?
If so try this experiment. Go to it. Climb it with just the truck in drive I at 55 mph. Record (or remember what gear it used.)
Now go back up it in 3rd gear. Notice how you can get to 55 and leave out of the throttle and then can actually increase speed with very little throttle input.
This is why it will run cooler in a lower gear in the Powerband. In a higher gear you have to dump more fuel to keep the RPM momentum. In a lower gear you can dump less fuel and therefore create less heat.
@silver billet nailed the explanation above.
Tow/haul pics the best gear based on fuel mileage and comfort.
Selecting the gear yourself allows you to just select for power.
My 99 V10 Magnum with 5 spd and a 3rd pedal could tow most every hill in 4th...even 5th...but put that truck in 3rd and it was a blast to throttle up the hill.
That said...also in 3rd...i knew I would not have to downshift for a turn...in 4th or 5th I would.
Does that make any sense? I hooe so.