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Nonlinear perturbations have significant consequences on excitation of surface waves on overdense plasma. Linear surface modes on overdense plasma appear at specific frequencies of the incident wave. By nonlinear considerations, however, this phenomenon takes place for frequencies different from frequencies of the linear regime. Here, to study the nonlinear effects on the modifications of the proper frequencies of exciting the surface modes, we consider the framework of the warm electron-fluid model and Poisson equation. We apply a perturbation procedure to linearize the nonlinear set of magnetohydrodynamic equations. Obtaining the analytical solutions at the first- and second-order corrections provides a powerful tool to perform our study. By employing proper boundary conditions, we derive dispersion relations for both corrections. The range of the allowed frequency of the incident wave that leads to the stable surface plasma waves is determined at the linear approximation. Then, at the second-order corrections, we investigate the nonlinear modifications of the dispersion relation of the plasma surface waves and find a new proper frequency region. We also discuss the influences of the presence of the nonlinearities and the thermal effects on the involved physical quantities.