When a liquid evaporates,particles of liquid absorb energy from surroundin to compensate the loss of energy during evaporation.
this makes surrounding cool.
In desert coolerwater inside it made to evaporate.
This lead to absorption of energy from surrounding.Again, we know that evaporation depends on amount of water vapour present in air.
If amount of water vapour present in air is less, evaporation is more .
On hot dry day, amount of watervapour present in air is less.
Thus water present in desert cooler evaporates more, cooling surrounding more.
THAT'S WHY,,A DESERT COOLER COOL WATER BETTER ON HOT DRY DAY.
hope it helps u......