Temperature does not affect the bounce of a rubber ball. Let's say you bounce a rubber ball on the grass. The result will be different then bouncing a rubber ball on a concrete surface. The result is different because you are using a solid, hard surface to bounce the ball with. But the temperature will not affect the bounce of a rubber ball. you can test it out for youself.
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First, consider that a bouncing ball is an elastic system, that is, it deforms and returns to its original shape. The process of returning to its original shape is responsible for the bounce, the faster it returns, the higher it bounces. For most solids, including a rubber ball, higher temperatures make it more plastic, or more easily deformed and less able to recover its original shape, therefore higher temperatures (hotter) will make the ball bounce less. Lower temperatures will make the solid more brittle or elastic, and make the ball bounce higher. These observations, however, are based on the assumption that the ball is solid and of uniform composition throughout. If the ball is hollow, the situation is much different. Within normal living conditions temperatures (about 10 degrees F to about 110 degrees F) the air inside the ball has a greater effect on bouncing. Low temperatures cause the air to become denser, thus reducing both volume and pressure inside the ball. This makes the ball partly deflate and when it is bounced, it deforms horizontally with little or no recovery, losing its bounce. At the higher temperatures, the air expands, increasing the pressure, thus the tension on the ball is greater and the bounce is significantly higher.
Let me also point out that the surface upon which the ball is bounced influences the system as well. A steel ball or glass ball represents some of the more elastic systems we know, and they will bounce very high on a solid surface with enough mass to resist the force of the ball. If you drop a glass marble on a marble countertop, it will bounce very high. Dropping the marble on a carpeted floor, however, results in the marble just lying there. Again, the function is elasticity, even to the point of being brittle, that creates the ability to return to form and bounce. A rubber ball, being plastic in nature and easily stretched and deformed, depends on its lesser mass and will bounce from a less-than-optimum surface for impact recovery.
Yes, temperature affects rubber. If you freeze rubber, it will become stiff, and if you heat it, it will soften and become more flexible.