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More thermal mass = less sudden fluctuation in temperature.
That means if there is a sudden cold snap, it takes longer for a large amount of thermal mass to cool off and become affected by the cold. If you remove thermal mass from your body, you become cooler and loose the added benefit of the thermal mass helping to keep your body from being as affected by a cold snap. When you first consume the water, your body needs to heat it. Once warm it acts like a reserve battery for the heat by being a heat-saturated thermal mass. When you urinate, you lose that heat and drain the battery. All of this is irrelevant to the fact that if you need to piss then piss. If you want to retain a bit of that heat, piss in a bottle and keep it in your sleeping bag at your feet until morning. Though, a bottle of hot water would be better. Even if it cools off to your temp, it will act as a thermal mass to help prevent cold snap problems for your feet.
Protip: staying properly hydrated helps improve blood circulation and help to better prevent frost bite.
