Rheological response in the presence of a rapidly changing temperature is an important problem, both as a basic study in rheology and as an applied problem in polymer processing. Here we carry out basic studies in which samples of polystyrene are simultaneously deformed at a constant elongation rate and cooled with linear temperature histories. Generalized time‐temperature superposition theory, presented earlier in the form of shift factors aT[T(t)], is considered further. We conclude that the effect of cooling rate R must be introduced explicitly, especially near Tg; a modified equation is suggested in the form aT[T(t),Tg(R)]. From a processing point of view, the most interesting result is that, at high cooling rates, the stress seems to be expressible in terms of a viscosity−not, however, one which is simply related to the shear viscosity.