This paper proposes a three-dimensional micromechanical model for evaluation of effective thermal conductivity of multiphase composite materials with periodic microstructure. The model consists in an extension of the parametric finite-volume theory which has demonstrated to be a promising tool for the analysis and homogenization of multiphase heterogeneous solids. The applicability and performance of the proposed formulation are examined through the solutions of different numerical examples of two and three-phase composites. Such examples consist of composites reinforced with unidirectional solid and hollow long fibers and aligned short fibers. In order to verify the effectiveness of the model, its predictions are compared with analytical and finite-element results, as well as experimental data. The results indicate that the proposed model is efficient and accurate in predicting the effective thermal conductivity of periodic composites and can be seen as a competitive alternative to other existing procedures based on traditional numerical tools like the finite element method. (C) 2019 Elsevier Ltd. All rights reserved.