Data of the analytical-numerical parametric investigation of a singularly perturbed temperature field in the boundary layer of the side of a rectangle on which nonlinear boundary conditions of the Stefan–Boltzmann type are specified have been given. It has been established that a nonuniform initial temperature distribution of the Gaussian type causes the appearance of “discontinuous traveling thermal waves” in the corresponding boundary layer. A set of parameters for which the “discontinuous traveling thermal waves,” being superimposed, lead to a local nonlinear enhancement of the thermal field has been found. This effect can be considered as “thermal resonance.”