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In this paper, the thermo-dynamic analysis of contact-impact problem is presented in the large deformation of hyperelastic material based on the Taylor-Galerkin method. The technique is applied for the time domain discretization of thermo-dynamic governing equations in the advection-diffusion problems. The impenetrability condition and frictional contact constraints are fulfilled by imposing the augmented-Lagrange technique for nonmatching contact surfaces. The Taylor-Galerkin method is employed to describe the advection-diffusion effect in the numerical solution of parabolic equation of unsteady heat transfer condition. The effect of temperature is taken into account in the stress field by...