We show that the Cooperative Free Volume (CFV) rate model, successful at modeling pressure-dependent dynamics, can be employed to describe the temperature and thickness dependence of the segmental time of polymers confined in thin films (1D confinement). The CFV model is based on an activation free energy that increases with the number of cooperating segments, which is determined by the system's free volume. Here, we apply the CFV model to new experimental results on the segmental relaxation of 1D confined poly(4-chlorostyrene), P4ClS, and find remarkable agreement over the whole temperature and thickness ranges investigated. This work further validates the robustness of the CFV model, which relates the effects of confinement on dynamics to pressure changes in the bulk, and supports the idea that confinement effects originate from local perturbations in density.