A long-time desert hiking friend and trip leader wrote a lightweight-hiking guide with the following advice for estimating the water you need. While YMMV, he hasn't lost anyone yet.
Assume 2 miles per hour over the whole route, on average
Add 1 hour for each 1000 feet of elevation gain
add 1/2 hour for each mile off trail / cross-country
Example: you're planning a 2-day, 25-mile hike with 4,000 ft. elevation gain and 7 miles of off trail hiking. 25 miles /2 days = 12.5 + 4 (thousand feet) + 3.5 (off-trail hours) = 20 hours.
Multiply according to the temp. Water weighs 8 1/3 lbs per gallon, so...
for cool temps -- .8 lbs per hour
for warm temps -- 1.2 lbs per hour
for hot temps (over 90)-- 1.6 lbs per hour
My own thoughts, in no particular order:
When packing a lot of water, IMHO, rigid containers (big gatorade bottles, etc.)pack and haul better than floppy platypi.
Water carried in your stomach counts -- if it's very hot I slam as much as I can, even to the point of discomfort, before starting out. I'm not uncomfortable for long, and feel more energetic over the long haul when I do this.
I do freeze my water bottles and if I pack my sleeping bag around them they will stay cold for a good long while. That said, leave enough unfrozen for the first several hours of your trip. It will eventually get warm during your trip -- adding powdered Gatorade or similar helps it go down a little better. However, you will get used to drinking it this way.
You'll need less water if you hike in the very early morning, take a nice, long, shaded siesta mid-day, and hike again in the evening.
When carrying 2.5 to 3 gallons I'll take a pack with a frame.
I feel less thirsty if I avoid too many salty foods.
Err on the side of too much water vs too little -- if you twist an ankle, get lost, or otherwise slow yourself down, you'll need the wiggle room.
Someone suggested caching water and / or keeping water in your car for your return. Both are great ideas and if you have a good cooler wrapped with an extra sleeping bag, block ice may last for two or three days in there.
I hope this is helpful -- forgive me if any of it was self-evident. And... have a GREAT trip!