it is already liquid if it is cooler water

It depends on the type of water cooler, but you can probably find the capacity at the bottom of the cooler.

Because the water is cooler the hot touch that you have causes the water to be cooler than what is is actually.

A water cooler usually refers to a water dispenser that chills the water. Some people also refer to a water fountain (one of those things you drink water from in public buildings or parks) as a water cooler as well.

cooler