Mindtools, codeine will dissolve very easily in room temperature water.
Some CWE methods suggest using hot water then cooling it down in the freezer; there is no point to this, as you may as well just use cold water from the tap in the first place.
Using hot water without cooling it down will result in more paracetamol going into solution.
ETA: Just saw your new post. I personally notice no difference between using the crash out method and using just water from the tap. If you are using tablets that don't dissolve that easily though, then using warmer water at first may be better.