A one-dimensional mathematical model of the heat transfer during evaporation of the liquid from the liquid-vapor interface located in a porous structure into the dry region between the interface and the solid heated surface is developed for the case when the vapor flows through the narrow dry porous zone along the heated surface towards the vapor channel. The model predicts the location and shape of the liquid-vapor interface, the overall heat transfer coefficient, and the heat fluxes which can be recognized as critical for the evaporator. The numerical results are presented for the case of the miniature evaporator for electronic components cooling.