The problem of statement of the heat problems of friction is under consideration. Solutions to such problems have been analyzed for three different variants of heat boundary conditions on the contact surface. At first, an analytical solution has been obtained in quadratures of a one-dimensional boundary-value problem of heat conductivity for a tribosystem which consists of a semi-space sliding on a surface of a strip deposited on a semi-infinite foundation. In the particular case of relative sliding two semi-spaces the solution has been integrated completely. It has been shown that the most general conditions of imperfect heat contact of rubbing bodies have been proposed by Barber. From these conditions it is possible to obtain (in limiting cases of some input parameters) both the Ling's boundary conditions of the perfect heat contact, as well as the Podstrigach's conditions of imperfect heat contact with the same division of heat between rubbing bodies. (C) 2012 Elsevier Ltd. All rights reserved.