We present a model to calculate temperature-relaxation rates in dense plasma mixtures. The electron-ion relaxation rates are calculated using an average-atom model and the ion-ion relaxation rates by the Landau-Spitzer approach. This method allows the study of the temperature relaxation in many-temperature electron-ion and ion-ion systems such as those encountered in inertial confinement fusion simulations. It is of interest for general nonequilibrium thermodynamics dealing with energy flows between various systems and should find broad use in present high energy density experiments.