Lots of bad or irrelevant info on this thread. Yes, you lose heat when you pee, since the pee is warm. However, you will have to pee inevitably, so you will lose that heat regardless of whether you pee immediately or after tormenting yourself for hours of holding it in.
As was mentioned, the body does not reabsorb urine once it is in the bladder, so you have already lost that fluid before you even pee.

There are some practical uses for urine, such as solar distillation or treating certain types of jellyfish stings, and perhaps even as a last ditch cleaning rinse for minor wounds since it should be sterile(this last one is an educated guess, please correct me if there is a medical reason not to do this).

I guess it would also make sense to apply urine to the skin or cloting to increase evaporative cooling in a desert situation, but if you're already sweating a lot I don't know if that would increase the cooling very much, and if you're not sweating then you probably are too dehydrated to have much urine anyway.

I don't think urinating on your hands to warm them would make much sense since the moisture would make them even colder after the brief moment of warmth.

Drinking urine in any way is never a good idea, it will only dehydrate you more and waste your body's resources.