How would you make deserts cooler?

On first reading, my thought was, "Just put it in the refrigerator" then I noticed there was only one "s" in desert. :-)

Deserts are hot and arid because historical weather patterns have dried out the topsoil and removed the nutrients from the surface. Once the vegetation is gone, all of the sun's energy is absorbed into the ground heating and cooling it faster than an area with vegetation.

In some areas, if you could replace the topsoil and build an irrigation system so that vegetation would grow you could possibly change the weather pattern. At least trees would provide shade and the vegetation would absorb some of the energy and hold the topsoil in place.

In other areas however, there are natural reasons for why the desert exists. The Atacama Desert in Northern Chile is on the edge of the Pacific and you can see rain clouds offshore but they never get close enough for the rain to fall on land because the height of the Andes mountains farther inland block the winds that would otherwise bring the rain ashore. To change that weather pattern you would have to literally move mountains.