The heat capacity of the human body is around 3.0kJ/kg°C, and the one of urine is likely close to water (4.2kJ/kg°C). As such when urinating a person loses proportionally way heat than mass.

So if you’re feeling hot perhaps relieving yourself might give you a bit more comfort. Although you’ll likely do it anyway, as you drink more water.

For faeces it’s trickier, as their heat capacity varies quite a bit depending on the moisture content, from 4.6 to 0.4kJ/kg°C. I’d guess that for healthy individuals it should be the same effect but in smaller degree as urine.

(And thus the No Poop Challenge becomes acclaimed as the solution for energy waste.)