Bill wrote, "Just to be sure I understand, it'd be for hot, low humidity conditions where water sources are relatively infrequent, to allow you to spread out the cooling effect over a longer period of time? I get cooled nicely if I soak the poly/nylon blend shirts I usually wear, but it doesn't last very long. Same amount of cooling per gram of water though, right, so I could in principle recoup by carrying some extra water and re-soaking the shirt? (Not that I'd want to, in preference to your solution, just trying to be sure I'm understanding the underlying science.)"
Another plug for linen: I live in the Southeast (central VA), and so experience a lot of hot, rather humid weather. If you compare the thermal conductivity of different common fabrics it goes like this from least thermally conductive to most; polypropylene, silk, polyester, wool/acrylic (silk, poly, wool, and acrylic are relatively close to each other) , nylon, linen, and cotton.
Where i live during the hot weather, you want something that absorbs and/or wicks moisture fast off your skin, and also releases it relatively fast, while being fairly thermally conductive at the same time. The only thing which fits this bill, in both my experience and research is linen (and hemp, these are very similar).
However, in the Sun, you want some thermal resistance. Linen has more thermal resistance than cotton because it has hollow fibers, and so it does insulate you some from the Sun as well--definitely more than cotton.
I've tried different types of fabric for those hot humid days, and so far my linen shirts seem to keep me the coolest of any. The next best that i've found is high nylon content with some cotton or tencel (so like 65 to 75% nylon to 35 to 25% cotton or tencel). However, untreated nylon is one of the fabrics most quickly broken down and degraded by UV rays.
Pure cotton i only like for desert like conditions of hot and very dry, but even then it's not ideal because there is so little thermal resistance, and processed cotton doesn't have much UV protection--unlike linen and hemp, which are naturally highly U.V. protecting and resistant. Linen holds water longer than the synthetic fibers (given similar thickness, weave, etc), but releases it noticeably faster than cotton.
There are probably good reasons why so many of the earlier Euro and American explorers of Africa and Asia typically wore light colored, loose fitting, and long all Linen clothes. Because it worked.
Plus Linen, like Wool, is great at controlling and minimizing odor. It is commonly known as the most hygienic fabric.