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I don't think the peeing to stay warm myth is true. Here is the general equation for heat transfer:
Q = -hA(Ts – T)
Q is the amount of heat transferred, h is the material constant, A is the surface area, Ts is the temperature at the surface, and T is the outside temperature.
Thus the rate of heat loss is proportional to the amount surface area (aka your skin). The only way that peeing could change this rate is if it affected the material enough to change the heat constant. This is unlikely as the material is your skin and not the rest of your body. Your skin is the primary insulator for your body and what is inside it should not affect heat loss. Now if you drink a cold drink you will of course lower your body temperature.
This is the same for an empty house or a full house or an empty fridge or a full fridge. As pointed out earlier the difference between full and empty is how long it takes to reach the stable temperature.
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