Contact between a liquid and solid surface, whose initial temperature exceeds the maximum value for which a surface may be wet, is restored during quenching. Due to the complexity of the process, the mechanism of heat transfer during quenching is still not sufficiently understood. A numerical simulation is carried out to study the features of heat transfer and rewetting front dynamics during quenching of the vertical overheated surface by the falling cryogenic liquid film. It was found that the initialization of the rewetting front occurs after lowering the surface temperature to the temperature corresponding to the thermodynamic limit of a liquid superheat. The results revealed that the maximum heat flux into the liquid during quenching is significantly higher than those in quasi-stationary conditions. The dynamic pattern of the running fronts obtained numerically satisfactorily correlates with the pattern observed in the copper-nitrogen quenching experiments. The numerical model allows us to quantify the quench front velocity and temperature fields in the heater variable in space and time. Knowledge of the quench front velocity and the full time of transition process is required for solving the important problem of nuclear reactors safety.