Since most polymer processing operations involve inducing flow at the same time that the material is being heated or cooled (so‐called ‘‘nonisothermal rheology’’), there is a strong need for systematic studies to develop nonisothermal constitutive equations. In prior work we pulled small (fiber‐like) samples in the rubbery state at the same time that we cooled them (up to 4.5 °C/s). In the present work constrained (clamped) samples were cooled rapidly from about 20 °C aboveTgto 20 °C below it, and the stress build‐up measured. Accompanying independent studies (to establish the relaxation spectrum) were done in a cone and plate viscometer in the rubbery state and in a Rheovibron in the transition and glassy states. As in the earlier (pulling) work simple time–temperature superposition of thetimeconstantsdoes not work: the measured stresses are higher than predicted at high cooling rates. Several efforts based on multiple or experimentally adjusted shift factors were tried but seemed implausible. We conclude finally that themodulithemselves must depend on thermal history. By using a plausible, but finally empirical, adjustment of the moduli as a function of cooling rate, both sets of experiments (the pulling data at high temperatures and the constrained stress data at lower temperatures) were brought together in a single framework.