New Global Warming Study Demonstrates That Climate Change Studies Are Hard to Understand

This new study, the latest "smoking gun" on climate change, purports to show that the earth is absorbing more heat than it loses and that this imbalance is higher than it's ever been and they measured this using new techniques like little sea-diving robots.
Ok - but wouldn't the earth have to absorb more heat than it gives off, because the earth doesn't actually create any heat of its own, and we're in the middle of space which is a vacuum so don't we need to accumulate heat? And how do they know the "imbalance" is high by historical standards when they needed some fancy technology to measure what it is today - so how the heck can they be so confident about what it was in the past? No doubt they've got all this covered in the study, but if they are right it's too bad because it's too confusing for people to understand it.
But let's assume the planet is warming dangerously - there's an easy solution. Nuclear power. We could replace all our coal fired plants, tear down those massive dams that cause so much water controversy, and charge up electric cars over night if we spent a few hundred billion dollars building nuke plants all over the place. But no-o-o-o - nuclear energy has radiation, and radiation is b-a-a-a-d, which I know because Jane Fonda told me so, so we can't do that - so the hell with it.