Physics BS and material science engineer here -
Maybe you better spell that out: Bachelor of Science.
Heat loss in space by a spaceship will be ONLY through radiation. Conduction and convection are essentially nonexistent in the vacuum of space. Whoever made that post about a thermos - space IS a giant thermos, you don't have to build one into your ship. Radiative loss will come from blackbody emission. Assuming a emissivity of .1 - .2 (typical for metals like aluminum/steel), the ship will lose heat at a rate of 52.37 W/m^2.
The ratio of the ship's volume to surface area will tell you more about how fast it cools down. As others have noted, cooling off is a much smaller problem compared to air.
I recall Apollo 13, the air going bad and the temperature dropping were both problems. They were about four days from returning to Earth, which gives a rough idea of the speed the temperature dropped.
Also worth noting is how fast you are going compared to the inertial frame in which the microwave background is isotropic. The faster you travel in space, the more blue-shifted the CMB ahead of you becomes. If you are travelling at a significant fraction of the speed of light, the CMB will be hot enough to heat your ship. At near-lightspeed, the CMB will be deadly x- and gamma-rays. [/quote]
If you're going a significant fraction of the speed of light, you probably have a propulsion system that keeps you warm... Also, a common solution to radiation (and running into the occasional subatomic particle or hydrogen atom) is an ice shield ahead of the ship. Particles hit the ice which captures the particle and the energy makes the ice evaporate, rather than the particle hitting the metal hull and causing problems.
Of course, this is all handwaved away typically, so don't sweat the science too much. There's always a bit of suspension of disbelief necessary for spec-fic.
It depends on your target audience. I'm reading recent Analog magazines, and I'm reminded how good SF is with the least amount of handwaving possible.
Oh, oh! On a slightly related question - how does heat loss in space compare to heat loss in a submarine completely underwater?
The subs I'm moderately familiar with have double hulls and some kind of insulation or material in between, but the environments are radically different. I've heard proposals that future starships might utilize submarine-like technologies in their construction and environments and, since it would be fairly easy to calculate the surface area of a modern submarine due to its shape, I'm kinda' wondering if that idea is such a good idea after all and thinking that getting rid of heat would definitely be problem.
The outer hull of a submarine is basically at whatever temperature the water is. The conduction (water is pressing against every point on the hull) and convection (as the hull heats water, the water rises and more cool water shows up to replace it) pretty much insures this. A submarine needs a double hull to have any hope of having the inside temperature be anything other than the water temperature.
I'm thinking a double-hulled spaceship would be done mainly for shielding against radiation, needed for longer missions outside of the Van Allen belts, such as to Mars.