Would putting a sprinkler on my roof help cool my home?
I think you will just waste a lot of water compared to the cooling effect that you get.

A better way to cool the roof is to change its color.  A roof with a clean, smooth bright white surface can reflect about 85% of incident sunlight and emit thermal radiation with 90% efficiency. This surface  will be only 9°F warmer than the outside air on a typical summer afternoon. For comparison, the surface of a standard gray roof that reflects only about 20% of incident sunlight will be 69°F warmer than the outside air.  See http://coolcolors.lbl.gov/.

Some buildings in California are now required to have light-colored roofs in order to reduce energy consumption for cooling.