Dear student,The cooling in water cooler is caused by the process called as evaporation of water.It cools better in a hot and dry day because there is a high temperature in hot day which increases the evaporation rate of water and decreases the humidity of air.Thus leading to dryness in the air.So, due to increase in the rate of evaporation of water, the water cooler cools better on a hot and dry day.Regards