I always found it interesting when people talk about life support being off, there's this idea that it instantly becomes deadly to be in those areas, when life support shutting down just means there will be no new support given in that area. What oxygen and heat remains will still be there for a while. A ship the size of the Enterprise would have oxygen and heat for hours before there would be any real danger.
One of the things about
Star Trek that bugs me is that it consistently shows life support failure to mean a) the ship getting too cold and b) a lack of oxygen asphyxiating the crew. Both of these are inaccurate aboard a spacecraft.
First, the temperature. A spaceship cannot easily lose heat. It's in the vacuum of space. We're all familiar with thermos flasks keeping things warm (or cold) by insulating the contents with a vacuum. Spacecraft can only lose heat by radiation, which is very inefficient compared to convection or conduction.This is why the space shuttle always had its cargo bay doors open in space – the inside of the doors were its life support radiators. Starships in
Star Trek seem to have magic technology that somehow means they don't need large radiators to cool themselves despite the extraordinary energies released by warp cores and impulse reactors, but either way, if life support fails the crew are going to
bake, not
freeze.
Second, oxygen. If we take the
Enterprise-D, even excluding its nacelles and assuming 25% of the remaining volume doesn't contain atmosphere – machinery, structure, deuterium storage etc – we're still looking at a total atmospheric volume of around
4 million cubic metres, and assuming she maintains a similar atmospheric composition to Earth around 800,000 cubic metres of that will be oxygen. A human needs around 0.5 cubic metres of oxygen a day, which means the
Enterprise-D holds enough air for its crew of 1,014 people to breathe oxygen for
about two years. That's without emergency oxygen supplies etc etc etc. Lack of oxygen isn't the problem. The build-up of carbon dioxide is, because that can rapidly become toxic even if there's still plenty of oxygen. The issue isn't that you can't get oxygen
in to your body, the issue is that you can't get carbon dioxide
out. But the
Enterprise-D is still vast – assuming people are breathing normally it'd take around
twelve weeks for carbon dioxide to build up to toxic levels, though without ventilation it could happen much quicker on a room-by-room basis.
TL;DR – if life support fails, you don't freeze and run out of oxygen. You cook and choke on carbon dioxide.