So I read this xkcd, and thought it was kind of cool. However, I showed it to my engineer father and physics undergrad brother and neither seem to find the explanation very convincing (though they don't dispute the conclusion; I'm in computer science hence my deference to their opinion). Specifically they think that the reference to the second law is misleading, and that conflating light and heat/energy is leading to bad arguments. How valid are the arguments presented in the blog and is the conclusion valid?

In case of bad link etc, the question at hand is what it would take to burn things with moonlight like you can do with a magnifying glass and sunlight. The author claims that you couldn't heat anything over 100 degrees Celsius with just lenses and moonlight.

Edit: Thanks to my conversation with Rodrigo, I basically want a slightly more technical explanation that I can show to someone with a scientific background, but that I should at least be able to follow the math in if possible for the claim that you cannot use lenses to heat something hotter than its celestial source (sun/moon)