This old technique calls back to legends of how ancient Egyptians used to stay cool on hot nights. Simply soak a sheet or blanket large enough to cover you in cold water, then wring it dry so it’s damp and cool, but not dripping wet. Then just use it as a blanket. As the water evaporates, you get the benefit of staying cool but not wet.
There are a few more common variations on this theme, like the cold washcloth or ice pack on your head or wrists while you sleep, or going to bed with cool, damp (but again, not wet) socks on to keep your feet cool and you comfortable enough to fall asleep.