Frictional or frictionless contact between bodies happens in every single day life. In this talk, one of dynamic frictional contact models, a thermoviscoelastic Gao beam with Coulomb friction dry law is studied mathematically and numerically. Since the frictional conditions are nonsmooth, a regularization technique is applied to approximate a nonlinear variational formulation. We prove the existence of weak solutions satisfying the regularized variational formulation, based on a priori estimates and results for a pseudomonotone operator. Then, we pass to limits, as a smoothing parameter tends to be zero, in order to show convergence results for the regularized formulation. The fully discrete numerical schemes are proposed in which a guarded Newton method is employed to compute fully discrete numerical solutions of a nonlinear system at each time step. We select several groups of data to present numerical simulations.