The paper presents results of a computational experiment simulating rapid cooling by falling liquid nitrogen film of an overheated vertical copper plate with a structured capillary-porous coating. A dynamic pattern of the running quench front was obtained, and it correlates satisfactorily with that observed in the experiments. The features of the heat transfer and quench front dynamics in the transient process are studied. The maximum density of the heat flux carried away into the liquid turned out to exceed by far that in quasi-stationary conditions. The presence of capillaryporous coating significantly affects the dynamics of quenching and temperature fields and makes it possible to reduce the total quenching time more than threefold. Initialization of a quench front on a plate with a structured capillary-porous coating occurs at a temperature much higher than the thermodynamic limit of liquid superheat. The reliability of the numerical simulation results was confirmed via direct comparison with experimental data on the variation of the plate temperature, as well as on the velocity and geometry of the quench front.