The NSA dedicates most of its resources to "working smarter not harder." If they have discovered a weakness in AES, it could be as little as running a single executable on a Macbook Air.
If by "working" you mean "bullying" and "strong arming" and "threatening" and "blackmailing" people. It doesn't take a lot of energy to bullying somebody into putting trojan horses into their encrypted email service, and threatening to arrest them if they shut down their company. What kind of dirt do you think they have on Obama and Pelosi and the rest of the Senate and House of Representatives, to make them so cooperative? More like "Work illegally, not smarter."
We do not know that. Using thermodynamics we can establish a limit on how much computation we can do (if I recall correctly Applied Chryptography says that a super nova does not have sufficient energy to count to 2^256 in base 2). However, we have no theoretical bases regarding how much computation is involved in breaking AES256. All we do know is that we (the public) do not know of a way to do it.
So what would the carbon footprint be of WikiLeaks releasing 50 gigabytes of encrypted random data?