For the most part they don't need active cooling. At near ambient temperatures and low humidity it's generally easy to keep cool assuming your in the shade and not actively moving. With a well designed house it's often stays in the upper 70's to low 80's even during extreme heat because the nights are often cold.

The real issue is many structures are designed to be actively cooled so they get much hotter than ambient temperatures which is an issue. The urban heat island effect also tends to make thing far worse for homeless populations.

People will also do things like fill a cheap kiddie pool with water under a tarp which will take the edge off. In extreme days you can even add some ice cubes to that, but just as heating a kotatsu is much cheaper than heating a room this is fairly cheap. https://en.wikipedia.org/wiki/Kotatsu

PS: I recommend using a comforter to make a low cost Kotatsu out of a computer desk in you use your PC near the window in the winter. You stay comfortable at a much lower room temperature.

Not having active cooling in the arid southwest US does not necessarily mean dangerously hot during the day. When night-time temps can hit the 50s and 40s in higher elevations, a house with decent mass can remain comfortably cool throughout the day if you ventilate properly at night.