This is a well-known phenomenon, and a proper explanation is needed. It seems counter-intuitive since common materials expand upon heating due to faster oscillation of atoms. There would be some reasoning to this observation with rubber that goes in opposite direction.
Here is Feynman's intuitive explanation: rubber contains very long molecules like chains. nearby atoms continuously hit this chains. of course you can imagine the stronger hitting be, the shorter will be chain. now heating rubber makes atoms faster, make them hit stronger which makes chains and so rubber shorter.