Bounce
Elasticity is what gives the ball its bounce. When a ball falls, it builds up kinetic energy (energy of motion). When it hits the ground and stops, the energy is transferred into the ball as it deforms and flattens out. The elasticity of the ball now has potential energy that rounds out the ball again pushing it off the ground. As materials become cooler, they become less pliable, losing elasticity producing less bounce.
Air Pressure
Air is comprised of molecules in constant movement. Warmer temperature results in more movement causing the air to expand. Confined inside a ball, air will push against the inner surface of the ball. The material of the ball will stretch from the pressure of the expanding air making it firmer. Warmer balls have more elasticity than cooler balls. Releasing a little air on hot days helps keep the ball at the right pressure.
Leakage
Not only does the material of the inflated ball become pliable in warmer temperatures, it also expands. The material used to make the ball is composed of molecules continually in motion -- the same as air. As the ball heats up and the material expands, the ball can leak small amounts of air. Over time, the material becomes slightly porous, allowing the air to be forced through the material with each bounce.
Damage
Over time, changes in temperature can weaken the ball. Using balls when they are cold and less pliable puts a strain on the material. When the ball is warmer and the material stretches again, weak area's can form and eventually start to separate from the seams of the ball. Balls are designed to work in warm temperatures. Subjecting a ball to high heat or cold will age and weaken the material, risking damage to the ball.