A battery's power, or the electrical current that it can provide, is greatly reduced when the temperature drops. A typical car battery, for example, has about 50 percent of its starting power at 0 degrees Fahrenheit when compared with its operation at 80 degrees Fahrenheit.
All batteries rely on an internal chemical reaction to produce an electrical current. When the temperature drops, the rate of this chemical reaction is slowed, thereby reducing this current. When trying to start your auto in winter months, the reduced current in a car battery is exacerbated by the fact that motor oil thickens in cold temperatures, thereby requiring more power to get the engine moving than when it's warm. Combine these two factors, and all car batteries reach a point as the temperature drops where they just can't start the car.
Conversely, when the temperature rises, this chemical reaction speeds up, and the battery's power is increased. A battery's overall life, however, is reduced at high temperatures. Even when batteries are not being used, there is always a small measure of discharge due to leakage between its terminals. As this chemical reaction is also temperature dependent, batteries stored in cooler temperatures can retain their charge longer than batteries stored in warmer temperatures.