I've done the TAT a couple times in triple digits and also was wearing Scout boots. Great boots but man my feet sweat! I just use plain cotton mid socks, I think I took a few pairs along and just switched them daily for fresh ones until I hit a motel to do laundry. I dont think it will matter what socks you wear with the Scout boots as there is no ventilation. They sure were nice and dry in the Colorado rain though!
Best investment on the trip was a can of Lysol to spray in the boots each night!