I'm not so sure about that. An atmosphere surrounding something may well slow thermal radiation, but you seem to be ignoring conductive diffusion and convection, both of which will draw heat off of something much more rapidly than radiation in a vacuum.
And both of which depend entirely on the conditions of the surrounding medium: they depend on the surrounding fluid remaining in motion, and are both severely hampered by a fluid with low thermal conductivity. We see this in ordinary cars all the time: coolant fluid has to be pumped through the engine block and the radiator to continue to transfer heat, AND air has to continue to move through the radiator to provide cooling. Thus your 99 Buick Jalopy runs a serious risk of overheating if you're stuck in gridlock in 105 degree weather, and god help you if you loose a fanbelt.
Conduction and convection is actually a much SLOWER process than radiation under most circumstances, thus nothing depends on those processes unless it's designed to move really really fast for a really long period of time. Mammals, for example, mainly depend on sublimation (sweat glands for humans, panting for dogs), as do a number of space suit designs and rocket engines.
I do recall "The Last Outpost" (as well as "Out of Gas" on Firefly), and I don't hold to either one's treatment of temperature loss. Both were written by English majors, not scientists.
Which makes virtually no difference, since the principal is sound. A starship without power has very few internal heat sources other than the bodies of the human beings inside of them. The starship's hull is going to radiate ALOT more heat than is produced by the crew and systems alone, especially once main power fails.
The flipside of the problem is scientists aren't always right either, and don't always bother to BE right, especially in science fiction.
As far as "The Last Outpost" goes, if we're talking about the ship's temperature being effected by power loss, then it should be getting warmer by your explanation, as they are above a class-M planet with a shirtsleeves environment the crew beamed down to, suggesting similar surrounding thermal environment as we have here on Earth
Only if Enterprise was physically
inside the planet's atmosphere. A planet with a venus-style greenhouse effect could maintain a fairly liveable temperature for quite some time, especially if much of that heat was being produced by effects in the planet's own atmosphere or the T'Kon energy collectors (whose maximum range is never specified).
If we insist on holding this scenario as infallible canon, then I make the following suggesting: Perhaps the energy draining effect was also draining the thermal energy from the ship's atmosphere.
Unlikely, since it also would have drained it from the away team and induced rapid onset hypothermia. As it stands, it only seemed to effect electromagnetic energy, namely phaser beams and electric potentials.
Another option; I seem to recall something about the Doctor ordering people to the ship's inner areas, perhaps transparent aluminum is much more thermally conductive than the rest of the ship's hull.
It would actually be simpler than that. If the ship is radiating all of its heat into space through the hull, then it will begin to cool from the outside-in. Bulkheads and crew spaces will provide some insulation, and again there's the fact that conductive heating is a fairly slow process as long as the working fluid isn't moving, so the last parts of the ship to freeze will be the parts farthest from the hull.
Also what's that crap about -70 degrees? You'd be frozen dead long before that point...
Actually, it takes a couple of hours of exposure to extreme cold to induce hypothermia, especially if you have some implements to buy time (thermal blankets, portable heaters, a hand phaser fired into your bowling trophies, etc). Suffice to say, they would be uncomfortable, but they wouldn't have frozen to death in the time it took for Commander Riker to save the day.
