In this paper the problem of cooling a component, in the interior of which heat is generated due to its work, was solved analytically. the problem of cooling of a processor with the use of a heat pump was solved based on a earlier theoretical analysis of authors of external surface cooling of the cooled component by using the phenomenon of liquid evaporation. Cases of stationary and non-stationary cooling were solved as well. The authors of the work created a simplified non-stationary analytical model describing the phenomenon, thanks to which heat distribution within the component, contact temperature between the component and liquid layer, and the evaporating substance layer thickness in relation to time, were determined. Numerical calculations were performed and appropriate charts were drawn. The resulting earlier analytical solutions allowed conclusions to be drawn, which might be of help to electronics engineers when designing similar cooling systems. Model calculations for a cooling system using a compressor heat pump as an effective method of cooling were performed.