The fart doesn’t decrease the body temperature, but it does (marginally) reduce your body mass, and therefore your body’s capacity to “carry” heat. If you’re hypothermic, your fart will most likely still be body temperature, as your core temperature remains at the correct temperature as long as possible, even sacrificing other areas if necessary.

If you’re hypothermic to the point where your fart is cold, it might be beneficial to let one rip if you’re entering a warmer area, so that your body no longer has to heat up the gas as well. If you’re somewhere cold, the fart probably won’t make a difference.