This is essentially the same problem as a full or empty fridge:
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It is definitely possible that peeing will help keep you warm, however, the reason is not that your body no longer needs to heat up your bladder (same argument with open vs full fridge). Maybe there are other things that happen after you pee like your metabolism changes causing you to burn more energy and create more heat. Or maybe you drank cold liquid before going to bed and your bladder has not reached your core temperature. Or maybe it is all in your head. Once the pee reaches your core temperature peeing will not save you energy but will likely let you sleep more comfortably. So I say go ahead and pee.