The rotor blades of gas turbine engines (GTE) are producted from the nickel heat-resistent alloys, in combination with embodiment determnining the admissible of working gas before turbine; this temperature has impact on the engine principial characteristics, such as thrust , economic efficiency, resource , etc. Nevertheless, these alloys do not guarantee the sufficient resistance to the impact of the aggressive medium of engine gas flow. The temperature in the interaction zone of saturating elements and the product basis in the course of forming the nano-coating of gas turbine blades is one of the main factor determining the chemical and phase composition of surface layers and concequently the physical and mechanical properties and perfomance of alloys with coating [1]. The paper present the general matchematical model (MM) of one-dimensional thermal conduction in multi-layers system of heterogeneous layers of spade covering, the lines of which relocate in time; the model comprises the general differential equations of termenal conductivity specified for every layers of the system, the terms of thermal contact of every pair of connected layers , and the terms of heat exchange on the outer edging surface of the system and the conditions of temperature destribution within the system before the beginning of every process stage.