It’s the other way around. Using the thermodynamics definition of entropy, dS = d(q_rev)/T, where S is entropy, q_rev is reversible heat flow, and T is temperature.
dS relates to stretching in that when the rubber band is stretched, the molecules have fewer configurations they can be in, so dS goes down. For a big T (i.e. heated rubber band), the dS is less than that of a small T (cold rubber band). In other words, a hot rubber band stretches less than a cold one.
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