TL; DR: I have left the most interesting and exotic way of getting energy at the end and the most plausive at before the last.
At the moment, scientific has already made some fusion reactors, the problem is that currently, they consume more energy to work than the produced by them, in addition, that they are very expensive and dangerous.
In order to fuse atoms, you need a high pressure or temperature, and any of both things can't be made in such a tiny space as an organ. Maybe with future technology, it will be able to reach the necessary pressure or temperature but I would be something so difficult (for the tiny space) that wouldn't be able to fuse many atoms per second, not very useful. Furthermore, fusion use to produce high energy particles like gamma rays, which are not exactly healthy for living organism nor some technologies.
You need something that doesn't need so extremes environments in order to be much smaller.
But you don't need to make exactly a fusion reactor, you could use other techniques like a cold fusion reactor to produce energy at room temperature.
Sadly, cold fusion is quite close to sci-fi technology than the real one, so there aren't many ideas of how to do it.
Luckily, there is something called muon-catalyzed fusion:
The biggest problem to fuse atoms is the "electromagnetic force field" that they have. The electrons cloud doesn't let two atoms be very close because both clouds are negatively charged, repelling themselves.
If you strip an atom from its electron cloud, it still has their positive charge from proton to repel them, but when atoms get enough close to be repelled by the electromagnetism, nuclear force gains priority and pulls from the gluons of both atoms in order to combine them.
If we were able to find a much cheaper and easier way to find muons and "inject" them into atoms we would be able to make fusion at room temperature. That is because of muons which are a different kind of electrons, much heavier than normal ones (207 times more heaver). Because of their mass, they are much closer to the nuclei of an atom, so it's easier to get close two atoms enough in order to combine them using the strong force. We just need a way to replace normal electrons with muon versions.
The muon, with a rest mass about 207 times greater than the rest mass of an electron, is able to drag the more massive triton and deuteron about 207 times closer together to each other [...]
Here it's explained the process.
Not actually a fusion reactor but it's the first time I've read about it so I wanted to mention. It's a special kind of fission reaction which doesn't high excited particles like neutrons or gamma rays, in order words, it's really safe (alpha particles are stopped by the skin, and beta particles by a thin layer of aluminium).
Also not actually a fusion reactor but still a worthy mention is the use of an RTG:
A Radioisotope Thermoelectric Generator (RTG, RITEG) is an electrical generator that uses an array of thermocouples to convert the heat released by the decay of a suitable radioactive material into electricity by the Seebeck effect. This generator has no moving parts.
That is great, it use decaying sustances (like uranium) and produce a constant flow of energy without maintenance (just more fuel). It isn't explosive, it doesn't need much cooling, it's perfect!
RTGs have been used as power sources in satellites, space probes, and unmanned remote facilities [...]. RTGs are usually the most desirable power source for unmaintained situations that need a few hundred watts (or less) of power for durations too long for fuel cells, batteries, or generators to provide economically, and in places where solar cells are not practical. Safe use of RTGs requires containment of the radioisotopes long after the productive life of the unit.
Literally, it turns the heat of the substance decay into electricity.
Basically, this device produces energy when it receives beta radiation. I'll transcribe a part of my most upvoted answer (I always wanted to say that!):
Diamond batteries are able to produce a low flow of constant energy for thousands of years. Sadly, over time the radioactive material start losing its power and the battery decrease it voltage over time (a bit similar to RTG).
I'll quote two paragraph of here:
These radioactive diamond batteries would have a very specific purpose – low power and extremely long life. A standard twenty-gram non-rechargeable AA battery stores about 13,000 Joules and will run out of power in about 24 hours of continuous operation. One diamond with one gram of carbon-14 would produce 15 Joules per day, much less than an AA battery.
But the power output of the diamond battery is continuous and doesn’t stop. The radioactive diamond battery would still be putting out 50% power after 5,730 years, which is one half-life of carbon-14 or about as long as human civilization has existed. During this time, the diamond battery would have produced over 20 million Joules. And would produce another 10 million during the next 5,730 years.
Also, you can see this five minutes video.
With enought technology, that could be very useful and luxurious!