Radiation-induced conductivity (RIC) of polyethyleneterepfthalate and polypiromellitimide has been studied experimentally and numerically in a broad time range from some microseconds to seconds at 103 K. It has been established that the charge carrier transport is dispersive with a low value of the dispersion parameter α (0.08–0.12). We have suggested a direct method of determination of the frequency factor of the Rose–Fowler–Vaisberg (RFV) model, which has been parameterized using computer simulations by the trial-and-error method. The main concern is a critical analysis of the existing theories of geminate recombination. It has been shown that the traditional RFV model is well suited to describe the RIC in studied polymers even at 103 K if due corrections to the notion of a free charge carrier and a non-Langevin bimolecular recombination have been made. The problem of a space charge field due to beam electrons stopped in a polymer sample, which is especially important at low temperatures, has been accounted for but not fully explained.