Two-dimensional direct numerical simulations and the linear stability analysis are performed for a flat-plate boundary layer in the Mach 6 free stream with the presence of local volume energy supply. It is expected that this technique can be used for the laminar flow control at high speeds where the second mode waves dominate. It is shown that the heat source produces different effects depending on its streamwise distance from the plate leading edge and its wall-normal distance. If the source is located upstream from the neutral point and its center is close to the boundary-layer edge, it reduces the second-mode growth rates and thereby diminishes the maximum amplitude of instability. If the source is shifted downstream from the neutral point and its center is within the boundary layer, the stabilization effect becomes weaker while the scattering of unstable waves by the source-induced non-uniformity of the mean flow comes into play. By variations of the wall-normal distance of the heat source located near the neutral point it was found that the maximal stabilization effect is achieved if the source center is near the critical layer. © 2014 Elsevier Ltd.