The water when evaporated from a desert cooler absorbs energy from the surroundings and makes the surroundings cool. Evaporation is inversely proportional to humidity. Lesser the humidity and higher the temperature, the faster is the evaporation. So on a hot dry day, the humidity is less. Thus water present inside the desert cooler evaporates more, thereby cooling the surroundings more. That is why a desert cooler cools better on a hot dry day.