We consider a viscoelastic solid in Kelvin-Voigt rheology exhibiting
also plasticity
with hardening and coupled with heat-transfer
through dissipative heat production by viscoplastic effects
and through thermal expansion and corresponding adiabatic effects.
Numerical discretization of the thermodynamically consistent model
is proposed by implicit time discretization, suitable regularization,
and finite elements in space. Fine a-priori estimates are derived,
and convergence is proved by careful successive limit passage. Computational
3D simulations illustrate an implementation of the method
as well as physical effects of residual stresses substantially depending
on rate of heat treatment.