A viscoelastic solid in Kelvin-Voigt rheology involving plasticity coupled with a heat-transfer equation through a temperature-dependent yield stress is investigated. No hardening is studied but the evolution of the plastic strain is considered to be rate-dependent. A numerical scheme which is semi-implicit in time and employs lowest order finite elements on weakly acute triangulations in space is devised and its convergence is proved by careful subsequent limit passage. Computational studies underline robustness and efficiency of the method and illustrate physical effects such as the softening of a material due to dissipated energy that causes a rise in temperature and a local decrease of the yield stress.
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