@QuantumBrick I should definitely state in the beginning that I am talking about hot temperatures, not the extremely low ones.
Also you stated (correctly) that the elasticity in climbing ropes does mainly come from how they are woven. So there the elasticity does not depend on atomic movements, but on movements of bundles of polymers. I very much doubt that on this scale at low temperatures (still >-100degC) there is no more unfolding.