Been watching episodes of Star Trek Voyager because I never saw the whole series and post ST:ID I decided I really ought to get fully up on the entire series since I've seen every episode of the original and ST:TNG a bajillion times.

Watching... the life support fails, or they need to divert power from the life support, and within minutes people start shivering and gasping for air.

Here's why this is nonsense, and I'm going to do this for an actual spacesuit and for a 'saucer section'. In space the only way to get rid of heat is by radiation, so if you're not further away from a Star then Mars your issue is going be cooking alive not freezing. But, sci-fi, deep space, yes you can freeze. But it takes a really long time. For a space suit, this freeze/suffocate thing can happen in a reasonable time line but for a space ship, no, just no.

The Saucer section of the USS Enterprise D has about a square kilometer, a million square meters, of surface area. We'll just assume the entire ship has 2 million to keep the math nice. We'll also assume they keep the ship at room temperature of 295 kelvin (22 C, 71 f). That means it should be dumping heat in watts equal to P = AσT^4 = (2,000,000) x σ x 295^4 = (2,000,000) x σ x 7.5 x 10^9 = σ x 1.5 x 10^16. Now σ = 5.67 10^-8, so P = 5.67 x 1.5 x 10^8 = 8.5x10^8 or 850 Megawatts. That's a lot of power, and that's the only figure that matter because anything else you're doing that needs power just ends as heat anyway. So barring the things outside the ship, like a phaser blast, no matter what you're doing that takes power is going to end up as heat inside the ship credit against that 850 MW. Shine a flashlight inside your ship and it gets absorbed as heat, shine it out a window and much of it escapes. Of course as big as 850 MW is, and it's enough to comfortably run 100,000+ luxurious modern houses, it's still kibbles and bits next to any sort of power requirement a ship would need and its roughly the heat produced by setting a half-dozen gallons of gasoline on fire every second. You never need to divert power to heat a spaceship because anything you need that power for inside is going to heat it just as effectively.

But screw, all power lost. How long will it take to cool down? First, as it cools it gives off less power, that whole fourth power thing, by the time it drops to chilly, 285 K (12C/54f) instead of 295, power will drop from 850 MW to 740 MW, and from 295 down to 273, 0C or 32f, 623 MW. Obviously neither is fatal. But the Enterprise D has a mass of 4.5 megatonnes. We don't know what the thermal mass is, it's mostly metal and metal usually has crappy thermal mass. But if we low-balled to .2 J/gK you could say that the ship would need to lose about a trillion Joules of energy to drop a Kelvin. Meaning to go from Room Temp to "Chilly" 54f, light jacket weather, it would need to shuck about 10 Trillion joules of energy at an average rate of about 800 MW, 12,500 seconds or about 3.5 hours. To go to freezing, which isn't going to kill anyone unless they're total idiots, will take longer, another 4 hours. And you can then assume you have a real problem, come hour 12 or so people will need to be donning arctic gear. This assumes no one finds any other heater of any sort to ameliorate effects. Now its assumed that their inertia-dampening and so forth might let them pretend their vessels have less mass when shoving them but its clearly still a lot of power because they run the damn ship on a giant anti-matter reactor, and to give an idea here, 1 kilogram of anti-matter combined with normal matter releases 1.8x10^17 Joules of energy, enough to keep the ship at room temperature for 59,000 hours, or nearly 7 years!. Alternatively that's power enough to produce a velocity of a mere 6.3 km/s for a 4.5 MT ship at 100% conversion to raw kinetic energy which is barely half Earth's escape velocity... and its not much different then what we have to burn to launch a modern shuttle. So in all probability they could just switch a damn shuttle's engine on and be warm.

They could also just start torching furniture, if everyone had around a ton of flammable shit in their quarters, 1000 people's worth, or at least a kiloton of flammable crap with each kg of that being good for around 1/20 of a second of your heat needs, so they've got 50,000 seconds or 14 hours worth of standard combustion, at the room temp loss rate, and at a very lowball value for a ship that has fairly luxurious accommodations and replicators. The damn ship has 50x times the mass of an aircraft carrier and 1/6th the crew after all. And mind you all of this assumes the ship isn't designed to be a giant heat storage and there's no reason not to build a ship that way and many reasons to do just that, so those 4 hours for a 10K drop are very pessimistic, assuming an average of .2J/gK when it could easily be 10x times that and thus ten times the duration for cooling. Point being there's no realistic scenario for freezing to death on one of these ships in under a day even if you sit around twiddling your frickin thumbs rather than busting out the matches or removing any of the blatant massive energy stockpiles on the ship.

By the way, to the inevitable 'we can't burn stuff because we'll run out of air', much like the suffocation thing that doesn't happen on a giant ship. That thing has at least 10 billion liters of air on it because volume-wise its mostly air, 2 billion of it oxygen, and again that's a serious lowball. That saucer section alone, if treated as a disc 400m in diameter, has a billion liters of air for every 2 meters of height. There are 16 decks in the saucer, at least 3 meters a deck, but it does narrow.

So 2 billion liters of oxygen and people use up 500 a day, a crew of a thousand uses up 500,000 a day... so that's oxygen for 4000 days, 11 years.

*"Captain! If we don't get the life support back on line we could suffocate in 11 years".

It does take a lot of air to burn stuff, its about as efficient as a human who again needs 500 L a day to burn about 2000 calories or about 10 MegaJoules of heat, so you would be burning your oxygen supply off at abut 40,000 liters a second. So would burn off that oxygen via combustion in under a day if it is that lowball 2 billion value.

Okay, so freezing or suffocating on a ship just doesn't happen on any reasonable timeline even with total power loss reduction to hunter-gatherer heating methods.

What about a space suit?

Well like a ship normally a space suit has problem overheating not freezing, but again in deep space, far from a star, its an issue. A spacesuit has about 2-2.5 square meters of surface area. If it starts at room temperature it's going to be shucking off around a kilowatt of energy a second. As long as you're breathing you're pumping out about 150 watts yourself. A 2meter surface area suit at 285 K (chilly) is pumping out 748 Watts minus your 150, or 600 W. Now humans are mostly water so a 80-90 kg person has about 360,000 J/gK, is going to take around 10 minutes to drop a degree even ignoring that their body will rapidly start producing more heat as it cools, since they're a warm-blooded mammal. As the suit temp drops you'll radiate heat slower and your body will ramp up production even if you don't start doing cardio exercises so you're not likely to freeze to death on a shorter timeline than your air supply even if you don't have battery-powered heaters. You certainly aren't going to freeze in mere minutes, and you won't buck-naked either. because you're losing heat at the same rate. You don't explode, your blood certainly doesn't boil, and you're not got to fly out an airlock then do the frozen-banana shatter thing. You will remain a warm flexible sack of meat for at least 5 hours because your body has about 13 MJ of heat above freezing temp and its going to take that long before you hit the freezing temp and still longer before the 0C water turns into 0C human popsicle. You'll be throughly dead and your extremities might cool faster but they're getting heat from your core by conduction which is faster than radiation in this sort of temp range. So it's like to be several minutes, if not hours, before your fingers could even break off.

There, </geek rant>