You should usen't use hot or cold water since they can break blood vessels on your face, in particular close to the base of the nose and on the cheeks. When they say cleanse with water, they actually mean rinsing the cleanser off with water, not using water as actual wash media.
What you should do is wash your face with cleanser and WARM water, and then splash cooler water once you're done.
What you should do is wash your face with cleanser and WARM water, and then splash cooler water once you're done.