It is impossible. The laws of thermodynamics won't allow perfect conversion of heat to other forms of energy. No matter what you do, you'll be left with some heat.

A biological process that converts heat to some form of stored energy like sugar, the same way plants convert light to stored energy through photosynthesis. If you make it based on biological life sciences instead of based on physical science, there are lots of options. Life processes do not follow entropy. They are the opposite of entropy, something that physics tends to ignore. The existence of the CN tower defies entropy. Life sciences, in fact, forced physicists to consider reversible processes.

Biology does not reverse entropy; it's bound by the exact same rules. Watch this video for an explanation.

@Phiteros Do your best to convince me that a bee hive has not reduced randomness and concentrated energy. Every single life process reduces randomness and increases energy. Given enough life, the universe would be completely organized and energy would be completely concentrated.

@JustinThyme It looks like you do not fully understand how entropy works. Watch that video. In a closed system, entropy can never be decreased. Yes, life can reduce entropy locally, but it does so by increasing entropy on a larger scale. In the context of this question, you have to consider the ship as a closed system. A plant could take in heat to create a sugar, but it can only do so by increasing the entropy (heat) of the whole system, aka the ship.

@JustinThyme Sorry, linked the first video in the playlist. This video is more relevant.

@Phiteros Apparently you do not understand how life works. Every chemical process TAKES IN heat (or other energy), exactly the reverse process than the chemistry occurs naturally. Entropy does not apply to life chemistry. That is why physics had to invent this thing called a reversible process - in other words, life processes.

You can never, ever, ever, ever decrease the total amount of entropy in the universe. At best, you can move it around, but that's assuming you have a perfectly efficient process.

That's what a reversible process is. You're not increasing entropy, you're just moving it around a little.

But a process can never be perfectly reversible. That would imply you have a process that has 100% efficiency. Sometimes in physics, we make approximations that an entropy change is sufficiently small so as to be negligible, but there still will be a tiny entropy change.

That's what my argument is. Yes, you can convert heat to other forms of energy. But the process by which you do so will never be perfect. You'll always have some heat left over. So even though you can eject some of your heat in this way, there'll be some left. The question becomes: does your heat removal process act faster than you produce heat?

In most cases, this answer can be "yes". I am really just objecting to the idea that you can perfectly convert your heat into other forms of energy.