Very simple idea: hydrothermal vents spew hot sulfur-rich water into the ocean. There are ever better maps of the biogeography of these vents, so we know where many of them are, how hot they are, and which kind of minerals they contain.
Harvesting the energy from this super hot water should not have
to be that difficult.
You let a stirling engine, encased in or made from strong steel, sink to the bottom of the ocean, and put it on stilts, over the vent. The "hot" part of the engine is put onto the vent. The "cold" part is facing up, into the colder water above.
The stirling is connected to a generator.
Everything is attached to a strong electric cable which reaches your ship at the surface.
Now you have electricity which you can use for several purposes.
1. desalinate water. A way of embedding the energy into a useful product.
Ship out the fresh water in big plastic bags to shores where it can be used to green deserts or for consumption by humans.
The big plastic bags are a cheap, existing technology. But it didn't come true that easily, because the sources of water that some of these companies wanted to tap, were off-limits (rivers, protected by conservationists, rightly so).
2. Alternatively, you can use the electricity to make hydrogen from desalinated water and ship that out.
3. Still a better alternative might be to use the electricity locally, to power remote underwater vehicles and drills to explore for minerals.
Apparently, the rocks of many of these hydrothermal vents (and the rocks in the vicinity) show high concentrations of valuable metals (gold, silver, copper, zinc, etc...) [see link].
EDIT: I just noticed there's a post titled "geothermal from hydrothermal vents". My idea is a tad different and more focused on ways to get the energy out. It's also less aggressive in certain respects. So I'd want to keep it instead of deleting it.