We study a flat laminar flow in the boundary layer of an electrically conductive incompressible fluid that has arisen near a vertical heated plate due to free convection with an arbitrary distribution of temperature or heat flow over its surface and under the influence of an acting magnetic field perpendicular to the plate, and the polyparametric method proposed in work. The derived universal differential equations of the problem under consideration are solved numerically on the ECM, in a one-parameter approximation, by means of the finite difference method, and analysis is carried out on the calculated and graphically presented results.