I view the stationary stuff in much the same light as the very close firefights. Any time the weapons move much faster then the ships in terms of acceleration and we assume they can't blow each other up in one pass then they might as well be portrayed as basically stopped and visually large, so that doesn't bug me as much.

Well that has two legit handwaves. 1) They're not really holding a natural orbit but basically just hovering above the spot because they have the engine power to do so. If you wanted to be right over the atmosphere but remain over the same spot, and your engines failed, you'd fall like a rock. Or, 2) They're in a stable orbit and someone just smashed them with a bunch of kinetic force. They're usually implied to be hitting each other with 'nukes or worse', so if your ship megaton suddenly absorb a megaton nuke it's going to change your position just like if you parked your one-ton car over a ton of explosives. Something in orbit's kinetic energy is really about the same as if you burned it's mas in regular combustive fuel, so hitting the enterprise from above with a H-bomb if its engines were off would shove it right down into the atmosphere and pretty damn fast. #1 isn't purely lazy either, if you've got away teams on a planet you presumably want to stay on the same side of the planet as them, but geosynch might be a bit too far away, tens of thousands of miles instead of hundreds of miles over the ground. If you've got the thrust to maintain that because it's equal or less to your normal drive thrust you may as well.

Mars is a bit of exaggeration, but first, Earth is not at its blackbody equilibrium, which is 255 K, or 0 Fahrenheit. A black bowling ball sitting 1 AU from the sun will be that temperature, a white one will be cooler. You can drop that to 21-220K or so if it's spending half it's time in Earth's shadow side, in low orbit. That doesn't apply to Apollo 13 but the equilibrium temp is still 255 K and that's uncomfortably cold to say the least... plus the hull's don't have a zero albedo so they don't absorb it all, same reason astronauts have white rather than black suits. Color and reflectivity are much bigger issues in space.

It's the difference of the factors involved. Take a thermos and throw it into space and it stays hot longer, because the IR reflects back in to the reservoir from the outer layer, paint the surface black or white and in deep space it doesn't matter but in planetary distances it makes a huge difference.

Edit: They key concept here is that on basic spacecraft you can't really increase your ability to get rid of heat, and you can't really make irregular surfaces as easily for a craft that will be flying through the atmosphere at hypersonic speeds, but you have a God Awful lot of heat spill over form certain things like your own engines, so you build to get rid of heat fast, for the ship, and you're stuck with that because and being cold is better then being cooked when you can flip a switch to get warmer off your batteries but not to get cooler.