[esarbe]

Just try to imagine the ludicrous amount of energy required to heat up the whole surface - and probably a good part of the ocean - by 2°C.

I think it is in the order of 10^17 joules or so.

[mr_mitm]

But that is distributed over a ludicrous amount of volume. These numbers are so large that I can visualize neither. How is this information supposed to help me?

[esarbe]

First I would check the number that I gave you and make sure it is correct. Then you put it into perspective; e.g. how many millennia would it take for a couple of hundred nuclear reactors to produce that much of energy.

Play with the numbers and see what you can learn about them.

Not sure you need to consider that much of a volume; we're talking about surface temperature, so you can just take an approximation of heat capacity of the surface of Earth.