We consider mathematical and numerical approaches to a thermoviscoelastic rod and nonlinear Timoshenko beam system with dynamic contact and heat exchange conditions. The end of a nonlinear viscoelastic Timoshenko beam is clamped while the another end is jointed with the bottom of a thermoviscoelastic rod. The top of the rod may come in contact with a rigid support. There are two conditions applied to the contacting end; Signorini contact conditions and Barber’s heat exchange condition. Indeed, the mathematical modelling is motivated by a Micro-ElectroMechanical System (MEMS). We formulate a partial differential equation (PDE) system with boundary conditions which describes the motion of the combined rod–beam with dynamic contact and thermal interaction. A variational formulation to the PDE system subjected to boundary conditions is obtained in an abstract setting and then a hybrid of several numerical methods is employed to the abstract formulation that guarantees to satisfy all the conditions at each time step. Convergence of numerical trajectories is shown, passing to limits as time step sizes approach zero. We derive a new energy balance form which plays an important role in establishing numerical stability. The fully discrete numerical schemes are proposed to compute numerical solutions and some numerical simulations are presented. This work is extended to a frictional contact problem with thermal effects, based on Coulomb’s friction law.