The air can be seen as a sponge which takes in more moisture as it gets drier. To change another word, while the air humidity goes down, the more moisture the air will absorb (or, the evaporation amount increases). Hence, under this situation, the cooling system gives a best performance to reduce the temperature.

But when is the optimal time in a day for cooling? In fact, when the temperature reaches high, the air intensity will loose accordingly, namely, the air is in low humidity. Therefore, we usually choose this period to work the system.

Then where does the heat(or the energy) come from while evaporating? In fact, everything the water touches is the source of heat(energy), which is why the temperature is down.