The temperature of the air does affect the bounce of a basketball. According to the ideal gas law, there is a relationship between pressure, volume and temperature. The pressure inside the ball is affected by the volume of air and the temperature. As the air temperature increases, pressure also increases.
Official NBA regulation basketballs should be inflated to 7.5 to 8.5 lbs. Filling the ball and storing it at room temperature helps to ensure that the ball remains at the correct pressure. For every ten degrees that the temperature changes, the ball decreases or increases its pressure by 10 lbs.