This design is fairly bad.
Just to open, the temperatures are wrong. Sea water freezes at approx -2°C, depending on the exact salt content. To get to -20°C and not freeze you would need a huge salt content.
Getting heat out at the central rod is a problem. You will need a set of fins at the middle with similar area to the inside of the cylinder. You will need a heat pump of some kind. You will need radiator fins somewhere outside the cylinder, to radiate the unwanted heat to space. Those will need shade from the sun, and will need an area comparable to the area of the inside of the cylinder.
And that process will use a lot of energy. Recall that, in the summer, you need to pay a lot for electricity to run your A/C. And you can't exactly generate electricity off the heat rejected by your A/C. You absolutely cannot generate power using this system. It will be a net consumer of power, by a wide margin.
Massively easier to control the desired temperature of the system by controlling how much sunlight falls on it. Say by a sunshade. And if you need to circulate the water you can just put in a fairly small pump.
If the goal is living space for aquatic life, you probably want the water to be in a layer on the inside of the cylinder. That way, the rotation can provide something useful in terms of an acceleration. You can then access the water from the inside surface, which can be uncovered if you want. The water is held to the inside surface by the rotation. You can provide heat, light, and the correct atmosphere inside the cylinder.