A class of nonlinear problems of non-stationary radiation-convective heat transfer under the conditions of microwave action with a small depth of penetration is considered in a forced laminar flow of liquid around a flat plane. The solutions to these problems are obtained using the effective asymptotic procedures at the successive stages of nonstationary and stationary radiation-convective heat transfer on the heat-radiating horizontal plane. The non-stationary and stationary stages of solution are matched using the “longitudinal coordinate-time” characteristic. The solutions constructed on such principles correlate reliably with the exact ones at the limiting values of such parameters as a small and large intensity of external thermal impact, small and large times, etc. The error of solutions does not exceed 1–7 %. As the plate is removed from the leading edge of the plate due to heat radiation, convective heat transfer degenerates from values characteristic of the boundary condition of the second kind to the values characteristic of the boundary condition of the first kind. A strong effect on the nature of variations of the surface temperature and Nusselt number of the complex parameter of microwave and thermal radiation is noted. An important advantage of the developed method for solving this class of external problems is that even before complex calculations it is possible to perform an exhaustive analysis of the fundamental laws of the processes under study. Despite a number of initial simplifications, the latter do not significantly affect the accuracy of results, guaranteeing reliable quantitative information. The developed method can also be extended to the regimes of forced convection with linear dependence of physical properties on temperature using transformation of A.A. Dorodnitsyn. To confirm adequacy of the constructed mathematical model, stationary radiation-convective heat transfer under the forced flow around a flat plate was studied experimentally. The results of comparison of the theoretical and experimental data show that they are in a good agreement. This again confirms the effectiveness of the developed method for constructing theoretical solutions to the nonlinear problems of forced convection using the asymptotic procedures.