This contribution deals with a heat conduction in a certain composite conductor with a deterministic structure, which is not periodic but in small regions of a conductor can be approximately regarded as periodic. The aim of this contribution is to formulate and apply two mathematical models for the analysis of heat transfer in skeletal rigid conductors. The formulation of the macroscopic mathematical models for analysis of heat transfer in these conductors will be based on the tolerance averaging technique (cf. monographs edited by Wozniak et al. (2008, 2010)). The general results are applied to the analysis of some special problems. It will be carried out validation of the obtained mathematical model by comparison of results from obtained tolerance-asymptotic model equations with results from finite elements method (Abaqus program). (C) 2015 Elsevier Ltd. All rights reserved.