A constitutive model is derived for the viscoelastic behavior of physically aged amorphous polymers under non-isothermal loading. The model is based on the concept of transient reversible networks, where a polymeric material is treated as a network of active chains (adaptive links) that break and reform because of micro-Brownian motion. The breakage and reformation rates for active chains in an aged medium are assumed to depend on the current temperature and the time after cooling below the glass transition temperature. To validate the model, the long-term viscoelastic response is predicted on the basis of data obtained in the standard short-term creep tests and compared with data from long-term experiments. Fair agreement is demonstrated between numerical results and observations. The model is used to calculate residual stresses in a polymeric spherical pressure vessel cooled down (after curing) to the room temperature. It is shown that physical aging of the polymer significantly affects stresses and displacements in the vessel.