Answer:
Boiling is the process where liquid (water) changes to gas (vapor) directly by no cooling process. As it's boiling, heat is being continuously give continuously so how can cooling happen?
But in the another way this statement can be correct too as evaporation too changes liquid to gas but does cools the liquid as high energetic liquid particles are escaping while leaving down the low energetic particles causing cooling.
To sum it up, boiling doesn't make any cooling.