Btw, instead of Antarctica, you could put your data centre in Iceland (with more or less the same pros, but fewer cons). And: people are actually doing that!
Iceland has a great geothermal power story, but the air is not nearly as cold. The reason Antarctica is good is because you would just blow outside air into the datacenter, no chillers required.
Yes, Iceland is a bit warmer than Antarctica. But cooling is still relatively easy: Iceland only gets to about 14C in summer days. Round it up, and say it's definitely below 30C.
If you run your computers at about 60C, that's still plenty of difference.
You can also look into dumping your heat into water. Either ocean or freshwater.
It approximately doesn't matter in the longer run and on a global scale whether you release your heat into the ground, atmosphere or sea. It's all conducted around sooner or later anyway.
Btw, instead of Antarctica, you could put your data centre in Iceland (with more or less the same pros, but fewer cons). And: people are actually doing that!