The act of increasing the pressure increases the temperature increases the temperature under the right conditions however once something has been pressurised, the temperature will slowly equalise with the surroundings to balance the heat absorbed vs heat lost. Waters relative impressibility also reduces this effect as the increase in temperature is basically coming from retaining all the energy that was in the volume of material and cramming it into a smaller space so you now have more energy per unit of volume. This is generally represented with the [ideal gas law](https://en.wikipedia.org/wiki/Ideal_gas_law) which, as the name suggests, doesn’t work in the same way to liquids like water
Because it is a fluid, there is flow that keeps the water at its maximum density at the bottom which for many liquids would mean the coldest material sinks and the warmest stays on top however water is a bit special as it has a maximum density at 4^(o)Cs so the coldest and hottest water want to rise leaving the bottom of the ocean at that temperature.
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