The analytical solution of a boundary-value problem of heat conduction for tribosystem, consisting of the homogeneous semi-space, sliding uniformly on a surface of the strip deposited on a semi-infinite substrate, is obtained. For materials of frictional systems: steel-aluminum-steel and steel-zirconium dioxide-steel, the evolution and distribution on depth from a surface of friction for temperatures and thermal fluxes, is studied. (c) 2008 Elsevier Ltd. All rights reserved.