Biggest issue would be power. Not sure what the geothermal situation is there, but given that they get most of their power from diesel, it's probably not great. You could build a big solar array, but then you can only use it for 1/3 of the year.
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!
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.