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The temperature dependence of the radiative exciton lifetime $(\tau rad)$ of J-aggregates of $3.3\prime -bis(sulffpropyl)-5.5\prime$-dichloro-9-ethylthiacarbocyanine (THIATS) characterized by a Davydov splitting of the exciton band has been determined over the temperature range from 4.2 to $130K.a$ The Davydov splitting of the exciton was taken into account during the calculation of the coherent length $(Nc)$ from the values of $(\tau rad$). The dependence of $(\tau rad$) on temperature was analyzed. The $\tau rad$ (T) of J-aggregates of THIATS can be rationalized within the framework of a 1-D excitation model.