For molecular systems in thermal equilibrium, the addition of energy. e. g. by mechanical work, can cause a change in entropy. This is known from the theories of thermodynamics and statistical mechanics. Specifically, both theories assert that the change in energy must be proportional to the entropy change times the absolute temperature. This rule is only valid so long as the energy is restricted to thermal states of molecules. If a rubber sample is stretched far enough, energy may reside in non-thermal states such as the distortion of chemical bonds and the rule doesn't apply. At low to moderate strains, theory predicts that the required stretching force is due to a change in entropy in the network chains. If this is correct, then we expect that the force necessary to stretch a sample to some value of strain should be proportional to the temperature of the sample.  Measurements showing how the tensile stress in a stretched rubber sample varies with temperature are shown in Fig. 4. In these experiments, the strain of a stretched rubber sample was held fixed as the temperature was varied between 10 and 70 degrees Celsius. For each value of fixed strain, it is seen that the tensile stress varied linearly (to within experimental error). These experiments provide the most compelling evidence that entropy changes are the fundamental mechanism for rubber elasticity.
The positive linear behavior of the stress with temperature sometimes leads to the mistaken notion that rubber has a negative coefficient of thermal expansion, i.e. the length of a sample shrinks when heated.  Experiments have shown conclusively that, like almost all other materials, the coefficient of thermal expansion natural rubber is positive.