In which hemisphere does the water get colder closer to the equator? Why?

Here you need to separate different concepts. The water itself should be the same everywhere, both in the south and in the north. But if you take into account the currents, it will be colder in the south. The reason for this is the current of the westerly winds, because nothing interferes with it (for example, the continents), and therefore these currents pass without problems into the Peruvian current (west of South America), and also in the west of Africa into the Bengal current, and then pass into the warm current … So it turns out that closer to the Equator in the southern hemisphere, the water becomes colder.