This paper has two objectives. First, necessary and sufficient conditions are given to characterize the uniform exponential stability of a sequence of c0-semigroups Tn(t) on Hilbert space Hn. Secondly, approximation in control of a one-dimensional thermoelastic system, subject to Dirichlet-Dirichlet as well as Dirichlet-Neumann boundary conditions, is considered. The uniform exponential stability and strong convergence of corresponding semigroups associated with approximate scheme are proved. Numerical experimental results are also presented.