Well, it's manga logic. Some WTF is expected.
Global warming is about the atmosphere, instead of radiating most the heat from sunlight to the space and cooling down, keeping it more and more within and heating up, due to the greenhouse effect caused by CO2 and other pollutants.
The root problem is in the air. Cooling deep water won't help.
Not to mention, water at seabed is already quite cold, at about 1 to -1C. And to cool down something, the heat needs to be transfer to somewhere else; if it's still in Earth then it's still the same.
Well, probably MC-kun gets some massive air purifier soon, and maybe his *** will become elixir to treat all kinds of disease?