Tire heat is generated not only by outside air temperature, road surface temperature, but also by friction of the tire against the road surface. Overinflating the tire will mean less road surface contact so it makes sense that there will be less temperature rise.
On the other side, a tire that is overinflated will ride rougher, provide less braking resistance and can be dangerous to the handling of the coach, as well as wearing out quicker in the center of the tread.
Follow the manufacturers chart for setting your tire pressure with the vehicle filled with FULL fuel, as well as loaded the way that you travel with all occupants and supplies. If you travel with water and waste liquid, make sure that is in place when you have the vehicle weighed.
