Building on permafrost is actually tricky with just residential levels of heat - houses are sometimes built on stilts in order to avoid melting the ground under them and making it unstable.

But I like where your head is at. Maybe an offshore platform? Alternatively, there are lots of places that aren't permafrost-cold which are nonetheless quite cool underground year round. I wonder how big a geothermal system would have to be to be an effective heat sink for a data center.