Nuking the Moon won't get anyone's attention, it'll just create more mess.
The 3rd rock around this star draws attention because it has copious liquid water, free oxygen in its atmosphere, and has both artificially produced light and sub-atomic particles emitting from it's surface. That should be more than enough to get someone's attention, if they happen to fly by.
If the civilization has achieved 100% energy efficiency, there would be no radiated heat, as that is simply wasteful.
Fundamental laws of physics apply, even if you're a technologically advanced civilization.
"Card readers? We don't need no stinking card readers." -- Peter da Silva (at the National Academy of Sciencies, 1965, in a particularly vivid fantasy)