The temperature dependence of the radiative exciton lifetime (tau(rad)) of J-aggregates of 3,3'-bis(sulfopropyl)-5,5'-dichloro-9-ethylthiacarbocyanine (THIATS) characterized by a Davydov splitting of the exciton band has been determined over the temperature range from 4.2 to 130 K. The Davydov splitting of the exciton band was taken into account during the calculation of the coherent length (N-c) from the values of tau(rad). The temperature dependence of tau(rad)(T) in units of (N-c)(-1) was compared to that for PIC aggregates. In contrast to the observations for the PIC J-aggregates [Potma and Wiersma, J. Chem, Phys., 108 (1998) 4894] the tau(rad)(T) of J-aggregates of THIATS can be rationalized within the framework of a 1-D exciton model.