From what I remember from Phoenix Protocol, it calls for cool showers, not cold ones.
As for the reason to avoid hot showers : sweating. Many people don’t think about sweating while showering, but a hot shower will heat up your skin, which will cause increased sweat.
When you’re dryfasting, you want to avoid any sudden losses of water( exercise, sauna, hot showers, etc). Your metabolism will create new water, but this process is slow but steady, always running in the background. So quick waterloss can be damaging.
The cold temperature slows down cell degradation as well as conserve energy and keep your body more dense which means stronger more grounded. It’s contrary to the dry fast. Slows down the dry fast. Under no circumstances should you do warm or hot water.