Stored deep in the entrails of Manhattan’s Metropolitan Museum of Art is an 8th-century caftan from the Caucasus region. It’s an indication of how long people have been turning to these lithe, single-piece slips to deal with warmer temperatures—modestly. Cut from airy material to sit off the body, a caftan is one of the coolest things to put on when you must wear something. In 100 degree-plus weather, said New York fashion consultant Nick Wooster of the billowy caftan’s appeal, “the last thing you want is [clingy] clothes on your body.”

Though...