Some basic reasoning tells us that cold showers can assist in weight loss. Consider the acute effects of a cold shower. The water hits the skin and almost immediately the body jump starts; blood flow increases, muscles harden, and heart rate increases. All of these things require energy.
It may help to think of the body as a heat engine. A typical heat engine utilizes a hot reservoir and a cold reservoir to run a motor, as in the diagram below. Only, instead of a motor, the body runs various metabolic processes.
Like a heat engine, the body must transfer heat to the environment. Even on a blistering hot day, we transfer latent heat to the air by sweating. Internal body temperature is the “hot reservoir” of the heat engine, while the “cold reservoir” is the air (or water) that surrounds the body. Without this transfer of heat, the energy of all our metabolic processes would have nowhere to go.
The key is that the metabolic output (W), equals the amount of heat flowing from the hot to cold reservoir. Taking a cold shower or bath forces you to burn more energy. And by estimating water temperature, you could calculate approximately how much.
In a 2.5 year experiment, rats of equal age were gradually accustomed to standing in cool water (at 23° C, 73° F) until they were standing in it 4 hours per day, 5 days per week. Even though the rats ingested 44% more food than the control group, their body weight was significantly lower. Incidentally, their lifespan was also slightly longer (by approximately 5%), and they had significantly fewer tumor formations .
This also trains your physiology to deal with colder temperatures, raising your resting metabolism. This is similar to the effect of physical exercise. The only difference is that while working out raises it through a direct stimulus to metabolism (through will power), showering in cold water is more of an indirect stimulus.