A bathroom is 10' X 10' X 8 feet. Your shower typically lasts 5
minutes and take 10 gallons.
At the same comfort level, you can trade off energy to heat water for
energy to heat the air in the bathroom.
What air and water temperatures are optimum to reduce overall energy
consumption.
Run your own tests to determine how hot the air must be to get away
with cooler water.
Bret Cahill