A thermodynamic framework is developed to describe a polymer melt undergoing glass transition that takes into account the fact that during such a process the underlying natural configurations (stress-free states) are continually evolving. Such a framework allows one to take into account changes in the symmetry of the material, if such changes take place. Moreover, the framework allows for a seamless transition of a polymeric melt to a mixture of a melt and an elastic solid to the final purely solid state. The efficacy of the model is tested by studying the fiber spinning problem for polyethylene terephthalate and the predictions agree well with the experimental results.