Keep in mind that there is a difference between staying hydrated, and keeping your core body temperature manageable (cool).
While water is essential to keep your body hydrated and functioning properly, that 6 gallons ain't gonna help as much as you'd like in keeping your core body temperature at a 'safe' level in such a hot environment if you are exerting yourself.
Consider this: if the air temperature is 120 degrees, how long do you think it is going to take before that water is 120 degrees? And that's assuming you don't do something silly like leave it in the sun in a dark colored pack/container, absorbing heat all day long. If that happens, then when you really need that water, you'll be hot, tired, sweaty, and thirsty - and that 6+ gallons of water you humped around all day is now TOO HOT TO DRINK.
Now, if that water were kept ice-cold (anyone have an ultralight 6 gallon backpacking thermos?), then sure, that water would do wonders at lowering your core body temperature. But if your core body temperature is getting high, drinking hot water is NOT going to bring it back down.
It sounds as if your 'plan' is to hike farther and faster so as to not need to carry as much water. But this will result in you overexerting yourself, raising your core body temperature, and putting you in much more danger from heatstroke. You need to stay hydrated, AND keep your core body temperature manageable.