In this article we conduct an overview of various types of thermal contact conditions at the sliding interface. We formulate a problem of non-stationary heat conduction in two sliding layers with generalized thermal contact conditions allowing for dependence of the heat-generation coefficient and contact heat transfer coefficient on time. We then derive an analytical solution of the problem by constructing a special coordinate integral transform. In contrast to the commonly used transforms, e.g. Laplace or Fourier transforms, the one proposed is applicable to a product of two functions dependent on time. The solution is validated by a series of test problems with parameters corresponding to those of real tribosystems. Analysis shows an essential influence of both time-dependent heat-generation coefficient and contact heat transfer coefficient on the partition of the friction heat between the layers. The solution can be used for simulating temperature fields in sliding components with account of this influence. (C) 2016 Elsevier Ltd. All rights reserved.