transpiration of trees and the cooling of the air The change from the liquid state of water to the water vapor requires a large latent heat to loosen the hydrogen bonds. The process of transpiration in the plant involves exactly this change of state. Here, the water evaporates from the lower leaf surface and the leaf gives up some of its heat. In this way, the leaf is prevented from overheating that would result from exposure to sunlight. Sweating in animals involves this same latent heat aspect of water.

If trees use transpiration to decrease their temperature, shouldn't the air around them  be warmer? The leaves are cooled as water evaporates, and the air should be warmer.

I always experience the opposite as I approach a forest. I'm not sure if the effect could be attributed to the reduced irradiation due to foliage.
You seem to misunderstand the thermodynamics of evaporation: "Evaporation is an endothermic process, in that heat is absorbed during evaporation." It appears you are confusing evaporative cooling with a heat pump. In a heat pump, the compression half of the cycle changes the vapor back to liquid, which does make things warmer.

Consider boiling water at sea level: Water liquid at 100°C becomes water vapor at 100°C, requiring ~540 cal/g energy to change state from liquid to vapor at the same temperature. At lower temperatures, as water evaporates, thermal energy is withdrawn from the liquid, cooling it below ambient temperature. "Swamp coolers" work on that principle.