More thoughts on hard science possibilities for interstellar colonization and the request to check my understanding of physics.
Suppose you have a fully self contained colony ship. They have some giant reactor producing power and as long as the reactor has fuel they can produce everything they need for life support on board. This could be with green houses to grow plants for making oxygen and food or it could also be pure chemistry. According to my understanding of physics, as long as it is a closed cycle within the ship all energy will eventually be turned into heat. And as they are in space the only way to lose this heat is through thermal radiation. The Stefan–Boltzmann law now gives a way to compute the energy the ship loses through thermal radiation. It only depends on the surface area of the ship and the temperature.
It seems that for a fixed surface area and a fixed surface temperature this gives the exact amount of energy the ship needs to use to be in a stable equilibrium?
If they use more energy the ship will heat up (which will also increase the thermal radiation), if they use less the ship will cool down (which will also decrease the thermal radiation). As thermal radiation changes with the 4th power of absolute temperature, there is some room for maneuvering but if the energy use is off by an order of magnitude or two in either direction, they have a problem.
Edit: Some specific numbers. In my last question linked above I learned that you need the energy equivalent of the entire energy output of the sun for a few days to accelerate a large space ship to half the speed of light. This means that if the space ship uses the equivalent of all the solar energy hitting the earth (around $10^{16}$ Watts) for life support and other internal energy needs that is negligible in comparison even over a timespan of decades or centuries. But if we assume a spaceship as a 10km cube and a temperature of 300 Kelvin the total heat radiation by the Stefan-Boltzman law above is only $5.67*10^{-8}*300^4*(6*10^8) W = 2.75*10^{11} W$. Meaning by my naive interpretation of physics they would need to use energy of that order of magnitude to not overcook themselves, for $10^{16} W$ they would need a much much bigger or hotter spaceship.