There are a lot of factors when it comes to water ambient temperature, body weight, exertion level and mathematics...you need between 16 and 24 oz. of water when exercising to remain hydrated. At 1 1/2 mph to the summit, that about 3 quarts of requirement to stay hydrated on the way up. Last night, I ran for about 30 minutes and lost 2 pounds...the equivalent to a quart of water. I perspire moderately.
I believe exertion is a bigger factor than temperature. When I did chute in May 2007 when the temperature did not exceed 40* F and was below freezing during the climb. I brought 4 L with me and drank 5 L...thank God for snow. All three of us were down to 8 oz. or less when we reached the summit.
Everyone has different requirements for hydration. There are no firm fast rules what you should take up with you. However, you should have enough with you in case you get stuck up there with injury or illness.