Heat-powered absorption cooling is an old idea. People had kerosene-fueled refrigerators back in the early years of the 20th century.
http://en.wikipedia.org/wiki/Absorption_refrigeratorhttp://en.wikipedia.org/wiki/Icy_Ball Some methods use ammonia and other toxic or flammable gases. But there's a known way to do it with just salt, air, and water.
1) Input warm, moist air into the system:
2) Sprinkle salty brine through warm, moist air. The salt spray absorbs water from the air and becomes brackish, and the air gets drier.
3) Sprinkle fresh water through warm, dry air. The water evaporates, and the air gets cool and moist.
4) Sprinkle salty brine through cool, moist air. The salt spray absorbs water from the air and becomes brackish, and the air gets drier.
5) Output cool, dry air
6) Regenerate salty brine and fresh water by heating and distilling the brackish water.
Plastic sheeting is cheap. I can make a solar still out on my deck that's a couple square meters, easy. More if I want to use the backyard or the roof. Plastic tubing is no problem. A small electric or wind powered pump to fill the water tanks so they'll sprinkle properly, and a fan to push air through.
A closed cycle system might be better. No risk from Legionella infestation, and no need to periodically dump out buckets of water. Hmm..