Raising the height on your mower during the heat of the summer lends shade from the taller grass blades. The shade helps to cool the growing point of the grass blade and the soil around it.
Grass clippings help to fertilize as they decompose, which happens rapidly during the hotter growing months. Grass clippings also help insulate the growing region of the grass blades.
It's best to water during the late evening and/or early morning hours. This keeps evaporation at a minimum and gives the water a chance to be absorbed by the grass roots before it can evaporate.