This is very important advice. Some more detail which you skipped over:
Radiation comes in two types: reflection and emission. The Saudi's have it right. Wear white clothes. Human skin and PURE white has an emissivity of approximately 1 (perfect). White has a reflectivity very near that of a mirror .9+ (near perfect). An aluminum or shiny mirrorlike thing, like a space blanket, is very bad. While reflection is high, emissivity is something like 0.1. Go out and feel a white car's paint (it will be cooler than any other color of car, by 40 degrees in 80 degree sunny weather) and the shiny chrome bumper (it will be burning hot). This is because chrome, mirrors, space blankets, have essentially 0 emissivity. What heat gets through the reflectivity cannot escape.
Blowing air over the surface is also extremely effective. I have an excel program which computes, correctly, heat build up, but not including the evaporative cooling effect. That effect is a type of convection effect. Above about 130 degrees, you cook. It's over.
These effects are all SURFACE effects. Treat your exposed surfaces and you treat the problem. Getting into water helps because the convection is inherently wet bulb. But white clothes or a white car is a good place to be. Get them wet and it will help a lot.
You incorrectly said "far less efficient" .. it depends on surface color and convection (the faster wind can cool as well as evaporation in still air). White vastly outperforms other colors in keeping you cool.
By the way, I said my program in Excel didn’t cover the evaporative cooling effect but it actually does. It just doesn’t input the effective rate of evaporation directly (e.g., 0–1) which could be the wet bulb temperature differential. There is a parameter for the rate of convective cooling associated with ‘wind’ speed. Here is the program: