I did an experiment where i placed a rubber band in water at different temperatures (-15°C till 90 °C) , and then a put a constant mass on the rubber band, to see how far it would stretch. What i noticed was that at higher temperatures (90 degrees) it would stretch further then at colder temperatures. I dont really understand why the increase in temperature allows for the rubber band to stretch more. because doesnt entropy dictate that at lower temperatures their is lower entropy and thus it should stretch more. Furthermore i compared my reserch to other studies but none provide an explation to what causes rubber to stretch more when a constant force is applied at higher temperatures? I would also like to mention that rubber bands do not follow thermal expansion so thus at warmer temperatures the moleculues become more tangled and contract,whilst at colder temperatures the rubber expands.
It's hard to say anything concrete without knowing exactly what material your band is made of, but I can at least propose one option. Rubber bands (and other polymers, etc) pass through a "glass transition" at a temperature below their melting point. As the material passes through this temperature (with temperature increasing) it transitions from a hard, brittle state to compliant state. In polymers, this is because at the glass transition temperature $T_g$, the free energy is sufficiently high to allow the molecular chains to slide past one another when force is applied. The transition is reversible, so the material will re-enter the brittle state at lower temperatures.
Now, rubber bands are typically made of natural rubber (polyisoprene), which has a glass transition temperature of -70C, but it's possible that the one you're using may have been made of a different material with a higher $T_g$. It's worth noting that the glass transition occurs over a fairly wide range of temperatures, so you may still be observing the tail of its effects even if you're still far from the "official" value for your material.
Half-baked molecular explanation: You're correct with your reasoning about the effects of entropy. At temperatures far greater than the glass transition (but still below melting), the rubber band will actually stiffen due to the entropic origins of its elasticity. However, the glass transition is a particularly obvious example of "kinetics vs thermodynamics" in nature. The brittle state is simply due to lack of energy to overcome the activation energy of polymer chains moving past one another. The equilibrium state is dictated by the entropic elasticity, but it can never get there on an observable time scale.
More Information: https://en.wikipedia.org/wiki/Glass_transition