Rutgers University has done a study about washing hands. The researchers put "high levels of a harmless bacteria" on the hands of 21 participants, multiple times over a six-month period. Each time, they were asked to wash their hands in water at a temperature of 60,79, or 100s degrees Fahrenheit (that's 16, 26, and 38 degrees Celsius) using varying amounts of soap.
The volunteers removed roughly the same amount of bacteria, regardless of water temperature. However, there was a marked difference in energy usage. Using cold water saves more energy than warm or hot water.

Washing for 10 seconds can remove bacteria significantly from hands. So washing our hands with cold water can save energy.