The gallon per day per person is the old rule and isn't too bad, but it's also old. If you use paper and burn it or carry it out it there will be less to wash. You can also clean pans by boiling stream water in them. You can use stream water for utensils and plates, just use lots of soap and wipe them, after they dry, with anti-bacterial wipes, you should rinse before use though. Any drinks that don't dehydrate you will replace water and I always take the Gatorade class drinks for that reason. Having said all that I would probably take about 2, 1/2 gallon containers. You will also probably have some ice melt that works fine for cooking if you clean and sanitize you cooler.
Beer can be a real downer when it's this hot and a good rule is to drink as much water or "ade" as beer during the heat of the day.