This contribution deals with the heat transfer in a certain elastic composite conductor with a deterministic micro-structure. This infinite two-phase hollow cylinder has in its cross-section periodic layout of inclusions in circumferential direction. These inclusions have constant width in radial direction, what makes character of material properties as radially graded. Therefore, we deal here with a special case of functionally graded material (FGM, cf. Suresh and Mortensen (1998)). The main aim of this contribution is to formulate and apply mathematical model for the analysis of thermoelasticity in such structures in order to obtain results taking into account micro-structure size also. Formulation of the macroscopic mathematical model will be based on the tolerance averaging technique (cf. Wo\'{z}niak et al. (2008, 2010)). The general results are applied to the analysis of some special problems for plane strain state. It will be carried out validation of the obtained mathematical model by comparison of results from finite element method.