Previous attempts to understand the mechanism responsible for the 1.4‐eV luminescence in solution‐grown CdTe:In were inconclusive because the measured combinations of injection level dependence, frequency response, and temperature dependence did not clearly indicate whether the transition originated from a band state or from a localized level associated with a compact complex. This paper reports the discovery of CdTe:In material in which temperature‐dependence data show that the 1.4‐eV luminescence transition cannot originate at a band edge. However, the spectrum, injection level dependence, and frequency response of the 1.4‐eV luminescence in the present material do not differ greatly from corresponding measurements on previous materials. The new data are presented in detail and include the first extensive measurements of the thermal broadening of the 1.4‐eV luminescence.