We introduce a new mathematical framework for the time discretization of evolution equations with memory. As a model, we focus on an abstract version of the equation partial derivative(t)u(t) - integral(infinity)(0) g(s)Delta u(t - s) ds = 0 with Dirichlet boundary conditions, modeling hereditary heat conduction with Gurtin-Pipkin thermal law. Well-posedness and exponential stability of the discrete scheme are shown, as well as the convergence to the solutions of the continuous problem when the time-step parameter vanishes.