The Reduced Relativistic Gas (RRG) model was introduced by A. Sakharov in 1965 for deriving the cosmic microwave background (CMB) spectrum. It was recently reinvented by some of us to achieve an interpolation between the radiation and dust epochs in the evolution of the Universe. This model circumvents the complicated structure of the Boltzmann-Einstein system of equations and admits a transparent description of warm-dark-matter effects. It is extended here to include, on a phenomenological basis, an out-of-equilibrium interaction between radiation and baryons which is supposed to account for relevant aspects of pre-recombination physics in a simplified manner. Furthermore, we use the tight-coupling approximation to explore the influence of both this interaction and of the RRG warmness parameter on the anisotropy spectrum of the CMB. The predictions of the model are very similar to those of the {Lambda}CDM model if both the interaction and the dark-matter warmness parameters are of the order of $10^{-4}$ or smaller. As far as the warmness parameter is concerned, this is in good agreement with previous estimations on the basis of results from structure formation.
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