One layer of solarveil actually has a lower UPF than a cooton t-shirt, blocking only 70% of the sun's rays vs. a tshirt which blocks 80. However, many use solarveil for its quick-drying coolness rather than sun-blocking properties. It is a synthetic fabric that sort of mimics the properties of cotton gauze.
For summer you will find most lightweight ring-slings fine. I wore my 2yo in a Maya wrap (even a black one in El Paso TX) without heat problems. There are certainly other carriers I prefer, and obviously polar fleece is out, but I think that saying "Cotton isn't cool" is too much of a blanket statement. I'm wearing a cotton gauze shirt right now that is much cooler than my cotton sweatshirts. Even in a fabric like wool, there is a lightweight jersey, mesh, lightweight summer suits, and heavy heavy wool sweaters.
For swimming I don't like cotton because it takes much longer to dry and stays clammy. If you're planning on taking it off as soon as you leave the water, though, any fabric will do. I have a TT cotton mesh and it's great. I've handled some of the lovely linens at sleepingbaby and I think they'd be super cool too. I do prefer synthetics for water use, but natural fibers for nearly everything else (although fleece is one of those strange hybrid exceptions).
As far as the UPF discussion goes, though, I think usually at least part of baby's body is sticking out, so focusing on clothing them properly is a more appropriate focus than getting a UPF sling, unless your baby likes to be completely enclosed.