The diet also suggests that by drinking more water, it will keep you full between meals and prevent you from over eating.
There is no evidence for any of this. Even if the body has to use extra energy to heat up the water, it's pretty minimal. Our body’s core temperature is very steady (unless we are ill) and the water just sitting in our gut is enough to bring it up to temperature.
There have also been studies around drinking water and fullness. While water that is trapped in food can help to fill us up (like in soups, fruits and veggies) because it increases the volume of the foods we eat, just plain water doesn't have the same effect, because our stomach empties too quickly with liquids alone.
There has been evidence for a placebo effect though, meaning that if you think the water will fill you up and you drink it, through the power of your mind, you will think you are fuller.
The diet suggests 8 cups of water on top of the water you are already drinking. The average person only needs between 8-12 cups per day to begin with. So unless you enjoy making frequent runs to the bathroom, I wouldn't encourage this diet.
Keep hydrated. It is important for keeping you healthy and alert, but don't hold your
breath if you think downing glass after glass of cold water is going to be the miracle weight loss solution.