Could you spell out the basic physics? I am having trouble connecting it to anything I learned in school. Biology/chemistry seems substantially more relevant.

To help heal the sunburn you must cool the skin. Aloe can only cool by a very small amount, as compared to running cool water.

Sunburn has nothing to do with temperature. You can get a third-degree sunburn in sub-freezing temperatures.

It has to do with UV-irritation, I believe. This guy might be talking about getting burned by the sun, perhaps by being too close ;)

Sunburn is inflammation of the skin. Inflammation is typically treated by cooling (e.g. when you put ice on a sprained ankle).

It's that first step that isn't clear to me. It may be the case, but it needs something other than physics to tell us that - and it doesn't tell us why slightly-cooler-than-lukewarm water is better than ice water.

You generally treat mild inflammation by cooling. The reason why you don't want to use ice water is because that will cool the outer layer of your skin to the point of pain before it's cooled the deeper layers significantly. Using slightly cold water means you can stay in the water for fifteen minutes easily, cooling all the skin layers well.

I thought this was common knowledge, i.e. basic first aid for burns in general?

My point was merely that "basic physics" doesn't tell us much here. You have to know that it's really inflammation that you're treating. You have to assume that cooling is the only contribution of the aloe (clearly, cooling isn't the only thing that can treat inflammation).

I mean, I know what's recommended as basic first aid for burns, and maybe that's common knowledge. The why of it, in enough detail, almost certainly isn't. Note also that aloe is quite commonly recommended as a part of "basic first aid for burns in general" following cooling.