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The world's oceans contain 1,335,000,000 km^3 of water. Heat capacity is 4.2 KJ / liter / C. So it requires 5.6e24 joules to heat the oceans by 1 C.

The world generates 20,000 TWh of electricity per year, and maybe 10% is for IT. That's 7.2e18 joules of electricity / year in IT.

So it would take 780,000 years to heat by 1 C. Or 780 years to heat by 0.001 C.

Other sources of global warming are far, far worse.

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The problem I'm concerned about isn't raising the average temperature of the ocean. The problem I'm concerned about is localized heating. Marine life is far more vulnerable to rapid temperature changes than life on land. We've seen dead zones developing in the past downstream of power-plants, as the warm water discharge from the steam turbines raises the temperature of the water and reduces its oxygen carrying capability. My concern is that if we put datacenters in the ocean, they'll create localized hot-spots with much the same result.

And that's if it was a closed system with no other sources or sinks of heat.

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