Looking for a pattern, that's why it takes an hour. You're looking for a pattern in the noise that repeats, then looking for subtle variations in the pattern to pick out the specific bits. There's a lot of other noise from other sources, but if you listen long enough, you know the length and frequency of the pattern you're looking for, you'll still be able to pick it out.
This won't work as something that happens in a one off, and you still need the target machine to be compromised to be repeatably getting the pattern to be created in the first place. That said, it is still impressive, and it shows that the target algorithm needs more randomization, which is the fix that was mentioned. I do this in firmware that I write, I don't hide the private keys all in one variable, I have them cut apart in pieces so that you can't just read my firmware and try every contiguous 4,096 bit block and see if it's my private key.