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The role played by molecular radiative processes after the decoupling of matter and radiation is discussed. In the physical environment of the expanding universe, molecules such as H2, HD, and LiH can be formed and contribute to the thermal evolution of the medium. In this paper, a detailed description of the primordial molecular chemistry is presented. The molecular cooling and heating functions have a slight influence on the decrease of the temperature of the matter. The diffuse radiative background due to radiative transitions of the primordial molecules is also calculated and found to be far below observational detection threshold.