Top comment is wrong: the short answer to the post title is a hard “yes” due to enthalpy of solvation. The process of fart mixing into ambient air generates heat.

The answer to your followup question would require some modeling — with the main factors being fart composition, body mass, thermal gradient, and room size.

Heat doesn't come from nowhere. If a fart increases the temperature of the room, then it must decrease the temperature of the body it escaped from.

So, if you're freezing, you should hold on to those little hugs of warmth as long as possible.

Mine tend to lower the temp of the room when everyone else flees to escape the smell.

People are missing that the fart is under pressure in the body. Increasing the gas volume from your colon to the room while keeping the mass of gas the same will produce a drop in mean enthalpy due to the reduction in mean gas pressure.

Extruded? Did you shit your pants?

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.

BTW, If one was already profoundly hypothermic, would it be unwise to fart?

Assuming the ambient air temperature is cold enough to induce hypothermia, farting is fine. Bringing cold air into the body is the problem. You'd be better off if you stopped breathing.

It does if you light it

Very slightly since your fart is your core temp, so you'll slightly lose some body heat but just slightly similar to breathing out

They were part of you that was already at a constant temperature. It would distribute the heat quicker but the overall heat transfer is the same.

One factor that changes this is that because your body maintains a constant temperature, releasing heat faster would cause your body to generate more heat to compensate.

This is an interesting detail, but there is akready so much written here, and lots wrong, that giving an answer that really helps would be way too much effort.

But in real world terms it really does not matter at all and you would have a very hard time even measuring any sort of effect.

surly the total entropy in the room will stay the same?

It's purely anecdotal, but my farts dramatically increase the overall temperature of my apartment. It's hell during the summer, but admittedly kinda nice when it's cold out.

Your a heat source but the fart is not. To any degree it has heat is from your body so you will cool as much as the fart is hot. So the fart will not increase the rooms temperature but your metabolic process is producing heat constantly causing you to heat the room constantly.

No. Heat is defined as average kenetic energy. It doesn't make a difference if that heat is in the atmosphere in a room, or in the body of a person in that room.