Around 8 p.m. on a hot Thursday in July, Nicholas Gubell, a driver for UPS, was nearing the end of his route on Long Island when he started to feel woozy.

That day, Mr. Gubell, 26, had delivered about 200 packages. Temperatures had soared into the high 80s, and it was even hotter inside the metal shell of the back of the truck, where, with each stop, he would spend up to a minute or so to retrieve his cargo, sweat beading on his skin.