All of the above. If you just wash with cold water you won't get the cooking effect on the curds necessary for a particular style. Even just a few degrees deviation from a recipe can drastically effect the flavor, texture, and paste. In general, the higher the temperature for cooking, the firmer the paste, like all of the thermo cheeses for example. However, that being said, there are lots of cheeses that are not cooked at all - Stilton & Lancashire for example. So.... if you wash with just cold water you would end up with a super moist, semi-hard cheese with a creamy paste. Sounds yummy. Give it a try. I would consider this a fresh cheese that will ripen quickly.
It's like making brownies. Undercooked they are soft and cake like. Overcooked they can be hard and crunchy.