  Structure-preserving integrators are in the focus of ongoing research because
of their distinguished features of robustness and long time stability. In
particular, their formulation for coupled problems that include dissipative
mechanisms is still an active topic. Conservative formulations, such as the
thermo-elastic case without heat conduction, fit well into a variational
framework and have been solved with variational integrators, whereas the
inclusions of viscosity and heat transfer are still under investigation. To
encompass viscous forces and heat transfer, an extension of Hamilton's
principle is required. In this contribution we derive variational integrators
for thermo-viscoelastic systems with classical heat transfer. Their results are
compared for two discrete model problems vs. Energy-Entropy-Momentum methods.
Such comparisons allow to draw conclusions about their relative performance,
weaknesses and strengths.
