I find it hard to buy the sort of shorts that I find coolest, so I end up making them. For me, it's 100% cotton in a calico weight cotton (like gingham, for example. Not see-through). I make elastic waist shorts for around the house with a wide leg (maybe 10cm of loose fabric at the hem) that come mid to lower thigh. These are bearable on days like today when it's going to be 35 degrees. I wear a cotton tunic in a cotton voile weight fabric on top. The tunic covers the waist so no-one sees the elastic waist.
Do I get kicked out of YLF for admitting to wearing elastic waist shorts? Oh, the shame.
When I'm going out on a hot day, I'll wear a cotton dress that hovers around the knee. I usually wear this with a longish necklace, like wooden or glass beads or a pendant that finish just above bust height. I've got a bit thingy about wearing sleeveless lately so I'll make it with sleeves, usually a shift or A-line dress with lots of room in the body. For me, this is the coolest thing I can find. We don't have air-con (we live off-grid with solar power) so I do what I can to stay cool. I plan on making one today in white for Christmas day, with white cotton lace sleeves.