The invention relates to safe operation support systems of nuclear power plants (NPPs) at severe accidents, including methods and systems for cooling and cooling control of the reactors molten core. The invention increases safety of NPP and cooling efficiency of the molten core of a reactor. The invention increases the efficiency of cooling the molten core of a reactor by safely removing the heat load from the molten metal mirror, ensuring the elimination of vapor explosions. The invention changes the principle of cooling the reactor molten core, in that after the molten core destroys the reactor vessel, the conditions for subsequent cooling of the molten metal are determined by the characteristics of the trap casing, but not of the reactor.