We study the evolution of a class of quasistatic thermal sub-differential contact problems with friction, for short and long memory visco-elastic materials, which can be put into a general model of system defined by a first order evolution inequality, coupled with a first order evolution equation. We present and establish an existence and uniqueness result, by using general results on variational inequality and first order evolution equation, with monotone operators and fixed point methods. Then a fully discrete scheme for numerical approximations and analysis of error order estimate are provided. Finally various numerical computations in dimension two will be given.