In this paper a detailed theoretical analysis is presented of the temperature dependent radiative decay in aggregates of pseudoisocyanine (PIG). Our approach extends the original linear exciton-phonon coupling model used by Spano, Kuklinsky, and Mukamel [Phys. Rev. Lett. 65, 212 (1990)] including static disorder and second order exciton-phonon interactions. It is shown that for a one-dimensional exciton model neither of these additional effects alone or in combination with linear electron-phonon coupling can explain the steep rise in radiative lifetime at 40 K observed in the J-aggregate of PIG. However, when the aggregate assembles into a two-dimensional bricklike structure its radiative dynamics can be simulated, with Linear exciton-optical phonon coupling as the only source for exciton scattering. Exciton-phonon scattering transfers oscillator strength from the k=0 state to other band states and also generates a nonequilibrium population among the exciton states, which persists during the superradiant decay. These effects together explain the marked temperature dependence of the radiative lifetime of the PIC J aggregate. When disorder limits the coherence length at low temperatures to a few molecules, as seems the case in several light harvesting complexes, the exciton population can equilibrate on the time scale of the superradiance. This situation pertains to the strong collision limit of the master equation, where the radiative decay is insensitive to details of the electron-phonon coupling, but only senses change in the thermal population among the exciton states.