Thanks, I was going to go through those same calculations, because I couldn't believe the numbers. In fact, I double checked your numbers (because I still had trouble believing) and came up with the same thing.
It's shocking to me that the energy accumulated by Earth from solar radiation is measurable in tonnes! Remember that the devastation from a nuke comes from a fraction of 1% of the mass of a relatively tiny piece of uranium.
To add a little more math, the atmosphere weighs roughly 5*10^21 grams. The specific heat of air is about 1 joule per gram-kelvin, so the solar radiance of the earth should raise the temperature 200 degrees centigrade each year if none was reflected or absorbed into the ground/water!
Even if you only assume the mass that this report claims is absorbed, it would add 2 degrees centigrade each year. Obviously some is absorbed into the ground, but either way it's clearly unsustainable. At some temperature, the Earth must radiate more than it is absorbing, otherwise we would burn up.
It seems clear to me that the temperature of the earth is going to be vary wildly depending on albedo/reemission, which life on earth affects by varying the composition of the atmosphere and surface reflection. This must be an influence on evolution - over the long run, organisms that tend to pull the temperature up when it gets too low and down when it gets too high would tend to succeed. By which I mean organisms that don't fit this profile would tend to wipe out virtually all life on earth, including themselves.
Maybe this is the cause of some of the extinction events in the fossil layers? It seems unbelievable that this hasn't happened before - some microscopic organism produces methane or CO2 in bulk and is very successful, then succeeds so well it fucks up the ecosystem for everybody.
It also looks like this is an existential test for humanity - maybe we can be the first multicellular organism to influence the temperature feedback loop enough to wipe ourselves out. Although I think it's more likely we'll just screw things up so badly lots of us die, until we lose the ability to influence the feedback loop enough to break it or we finally get the sense that our actions matter globally.