During evaporation, temperature of the water does not remain constant.
True
Evaporation is the process where the molecules at the surface of a liquid gain enough energy to break away from the surface. They become gaseous.
Think of molecules like tiny balls in the picture. In a liquid, the intermolecular forces are stronger than gases. So the molecules are trying to pull each other, trying to hold together. But some molecules at the surface are able to break away from this pull. When they break away, they reduce the temperature of the liquid.
This is why we sweat when we are hot. So that it will reduce our temperature when the sweat evaporates. And this is how clay pots are able to keep the water cold. Obviously, the temperature of the water does not remain constant when there is evaporation.