The results of modeling the processes of thermal destruction of large-sized space debris objects due to aerodynamic heating and melting in the upper atmosphere are presented in order to determine the feasibility of using a combined method for their de-orbiting. The cylindrical and spherical models of space debris elements were considered to estimation of the parameters of thermal destruction. The guess, that melt layer which is formed on an object surface, is carried away by a running atmospheric flow, was assumed. The value of heat flux depends on the location on the body surface, thus, two cases were considered: stagnation point, where the heat flux is maximum, and the point on a flat surface. It is shown that the efficiency of destruction of cylindrical bodies (first stages of launch vehicles) depends   on   the angle of attack during object movement in the atmosphere. The most advantageous, to provide the maximum thermal load, are the angles of attack not less than 40°. At small angles of attack, the thermal load on the side surface is insignificant, which can lead to incomplete destruction of the object. Calculations also showed effective combustion of objects spherical shape (fuel tanks of upper stages in the atmosphere. The presented trajectories of deorbiting of space debris objects confirm the effectiveness of thermal destruction for reentry angles: 0°; 0,5°; 1,0°; 1,5°. At the same time, the melting rate increases when reentry angle is increasing. Complete thermal destruction (melting) of the discharge objects is possible for the structural material from aluminum alloys, in particular АМг6. This case takes place in aerospace design practice. Thus, the use of a combined method of deorbiting the large-sized space debris into the dense layers of the Earth's atmosphere is quite appropriate, because it provides the productive aerodynamic heating and thermal destruction in the atmosphere some objects like as used first stages of launch vehicles or fuel tanks, which are the most typical components of space debris