Humans have a few intuitions about how temperature, heat, and liquids work. These intuitions lead us astray for the specific case of a bladder full of urine.
"Keeping Warm" / "Cooling down"
The first intuition is that things cool down on their own: If you leave a pie from the oven on your counter, it eventually cools down to room temperature.
We believe things cool down (and thus must be "kept warm") because ambient temperature is nearly always colder than any object which we consider to be warm. In reality, things only cool down when their temperature is higher than the temperature of their surroundings.
This is thermal equilibrium: in the absence of other processes, an object and its surroundings will eventually match temperature.
Does this principle of things cool down on their own apply here? No. Urine in your bladder is already at thermal equilibrium with the rest of your body.
We also intuit that liquids are colder than normal matter, because wetting your hands results in a very high surface area-to-mass ratio, causing rapid evaporation. Evaporation is a cooling process, of course.
We also think liquids are colder because they tend to have good thermal conductivity. We perceive the temperature of an object based on the rate of heat exchange with it; that rate is determined by the difference in temperature and its conductivity. Thermally conductive things feel warmer or colder than their nonconductive counterparts because they "move" heat more quickly. This is why metal objects at room temperature feel colder than e.g. cotton at the same temperature -- they are the same temperature, but the higher-conductivity object exchanges heat more quickly. It's also why you can put your hand into a 450 F oven without getting burned, but can't safely grab a metal pan at the same temperature.
Do these properties of cool liquids apply here? No. Urine in your bladder cannot undergo evaporation (it's a closed system), and its high thermal conductivity is irrelevant because it's already at the same temperature as the rest of your body.
There are only a few factors we need to consider to determine the nighttime temperature of a camper in a sleeping bag:
- Starting heat energy: How much thermal energy are we starting off with? Going to bed cold is going to be worse than going to bed warm. Starting with a hot water bottle in your sleeping bag is better than starting with a bagful of ice in your sleeping bag.
- Insulation: What is the thermal conductivity between the sleeping bag and the surrounding environment? Well-insulated bags are better than poorly-insulated bags
- Exterior temperature: How cold is the surrounding environment? All things equal, colder exterior temperatures will cause a higher rate of heat loss.
- Endothermic / exothermic processes: How much heat is the camper generating (e.g. from metabolism)? Humans convert chemical energy (food calories) into heat; if we burn more calories in this process, we'll stay warmer.
This leaves us with two possible physically-possible mechanisms of action for the "full bladder makes you colder" hypothesis:
- Endothermic reaction: It's in theory possible that urine undergoes some endothermic chemical reaction, like a one-time-use ice pack. There's no evidence for this happening; urine does not meaningfully change chemical composition over time when sitting in the bladder.
- Exothermic inhibition: It's in theory possible that the human body inhibits its own metabolism when its bladder is full. It definitely seems like we'd notice if this were actually the case. Either way, the mechanism of action here is not that we are "keeping our urine warm".
Running the numbers: A Sanity Check
The original claim is that you don't have to "keep warm" the contents of your bladder. We've shown that this isn't really a thing, but what if it were? A healthy full adult bladder is about 300 mL of liquid, which would weigh about 300 grams (or half a pound). For a hiker weighing 80 kg / 175 lbs, that's about 0.3% of your total body mass. Is a 0.3% change in body mass really going to significantly change your overnight heating situation? That's implausible at best. Note that the change in surface area (assuming you expand with a full bladder, rather than simply compress other parts of your body) is going to be smaller than 0.3% because surface is a quadratic measure but volume is cubic.
If this effect were actually noticeable, it should be twice as strong for taking a normal #2 (weight 1-3 lbs) right before bed, because you should have to "keep warm" your poop just as much as your urine (presumably). No one seems to comment on this. Humans are pretty good at sensing their bladder fullness but not great at sensing bowel fullness when it's within normal parameters, which suggests there's a strong psychological component going on here.
What about a hot water bottle in the sleeping bag with you, a common suggestion? Does this matter?
If we heat up a 1 L bottle of water (1,000 grams) to 100 C (boiling) and it eventually cools to 24 C (74 F, a rough guess at the temperature in a warm sleeping bag), we've added 76 Calories* of heat to our system. Basal sleeping metabolism is about 80 Calories per hour; nearly all of these Calories turn into heat (only the small portion stored as chemical energy, e.g. ATP, don't). So if the water bottle cools down to ambient temperature within an hour (a decent guess), it's almost as good as having another human zipped up in the sleeping bag with you for the first hour, which is definitely something. There's a throughput trade-off here; if you insulate the water bottle a bunch to make it cool down over twice the period of time, you get half the per-time energy output.
* Note Calorie, equal to 1,000 calories