This question was prompted by my answer to Under what conditions does heating a backpacking tent artificially make objective sense?. In my answer, I mention the possibility of hiking across Antarctica during the winter to experience the harshest cold that our planet has to offer.
You are on this Antarctic winter hiking trip, and you are chasing the cold. You know that the record cold is approximately -135F (-95C), and you are expecting you probably will encounter close to that, and you need to prepare for the possibility of a new record being set so you want to be safe down to a few degrees below that in case of emergency.
To assist in keeping safe, you build a snow cave. Though emergency snow caves are often not done correctly, let us assume that you did construct one correctly on this trip (ie: top of door below inner floor to trap heat, properly placed ventilation, doorway plugged up, etc.)
Normally, I hear people say that a good snow cave can keep the inner temperature at a pleasant freezing (32F, 0C) temperature even if the air outdoors is crazy cold. Would this still hold true at -140 degrees? At what point is it just so freaking cold that even a snow cave cannot be kept warm?
The amount of snow that is insulating you does obviously matter. Let's say you dig into a small embankment, so part of it is more than a few feet thick. For the front of it where you dug into the bank and had to then patch up the front of your cave, I would personally assume a few inches at most, as I have read about safety concerns of cave-ins when people craft thick walls. If you are not concerned about such a cave in danger, then feel free to assume thicker if that is truly what you would do.
Assume that there is a modest wind. Enough that heat does not linger well around objects, but not enough to worry about the integrity of the snow cave.
So, what is the minimum temperature at which a properly constructed snow cave can no longer be expected to maintain a constant 32F/0C temperature without artificial heating?