We study heat transfer through a composite with periodic microstructure. The thermal conductivity of the constituents is assumed to be temperature-dependent, and it is modeled as a polynomial in terms of the temperature. The thermal resistance between the constituents is taken to be nonlinear. In order to determine the effective thermal properties of the material, we apply the asymptotic homogenization method. We discuss different approaches to determine these effective properties for the different volume fractions of the inclusions. For high volume fractions of the inclusion, we apply the lubrication theory. In the case of low volume fractions of the inclusions, we apply the three-phase model. Comparing some special cases of our results to existing ones in the literature shows a good accuracy. (C) 2017 Elsevier Ltd. All rights reserved.