Cool the person?
Even in the tropics (Malay Peninsula, Barbados) and Southwestern desert the night air is cool enough that I can sleep well enough outdoors in a lightweight net hammock. Cost me about $8 forty years ago and rolls up into a package about the size of a baseball. Most often the difficulty is finding two places the right distance and strength to tie the ends.
I don't think my body needs to be brought down to the freezing temperature of water for me to sleep. But I lived 30 years before A/C was the norm (my parents 60 years, my grandparents never saw it) and that includes living in the Deep South.
I do admit sometimes sleeping in a tub of water. Evaporation takes away the heat well enough, even when air temperature is in the 100s F.