Polymer materials are well known to be sensitive to strain rate and temperature. Self-heating and friction effects also play an important role in the mechanical response of these materials. Numerous constitutive laws and phenomenological models have been developed to take into account these dependencies. This article proposes a simplified phenomenological model based on a mapping technique for the strain rate and temperature dependence. The effects of friction and adiabatic heating are also analyzed in this work. Relatively good results are obtained compared to experimental results for polypropylene and polychlorotrifluoroethylene. A parametric investigation of the effects of the interfacial equivalent stress (between the specimen and the compressive bars) and the fraction of plastic work converted into heat was performed. This parametric study allowed for a good approximation of these two parameters for the two studied polymers. POLYM. ENG. SCI., 55:2474-2481, 2015. (c) 2015 Society of Plastics Engineers