You can be secretive all you want, but it's extremely difficult to hide massive heat exchanging systems and/or generators from aerial/space photography. Particularly at the scale of an AWS-like datacenter.

Building a fully camouflaged datacenter could be done at much greater cost, but you still can't hide its thermal emissions from infrared. Basically every watt hour used in a datacenter environment turns into waste heat ultimately rejected into the atmosphere (except for the 0.000000001% that leaves the facility as photons down a fiber), so if you have N megawatts of waste heat from a rectangular shaped building located on a 300 x 400 meter sized plot of land, it's going to stand out.

Wouldn't it be possible to pipe away the heat to the next city and use it as heating there? That way the heat emissions wouldn't be as noticeable

> except for the 0.000000001% that leaves the facility as photons down a fiber

Realistically you're getting photons returned too.

Geothermal exists, but you would have to take care to design accordingly and even then there are plenty of other ways for a state actor to locate you. It probably doesn’t make much sense to spend money trying to hide from state actors; it’s probably better to (1) avoid conflict prone areas to the extent possible and (2) make it expensive for an attacker to shut you down (use more smaller data centers within a sensitive region, put some of them underground, etc) or (3) accept the risk of data center disruption.