During electron beam evaporation of liquid metals, the strong energy input induces strong temperature gradients along the free surface and in the interior of the melt. Thus, the liquid metal is subject to both thermocapillary and natural convection. The vigorous convective motion within the melt leads to highly unwelcome heat losses through the walls of the crucible. The strong convective heat transfer limits the temperature rise in the hotspot and, therefore, the thermodynamic efficiency of the evaporation process. The present paper aims to demonstrate that melt flow can be effectively controlled by using external magnetic fields in order to considerably reduce the convective heat losses. We employ numerical simulations based on the finite-element-method to study the effects of a traveling magnetic field on convective heat transfer in a liquid metal heated locally at its free surface.