This paper examines the influence of four different porous hosts (lightweight aggregates (LWA)) having different pore structure features, as hosts for phase change materials (PCM). The porosity and absorption capacity of the LWAs significantly influence the composite thermal conductivity. The incorporation of 5% of PCMs by total volume of the cementitious system reduces the composite thermal conductivity by >= 10%. The fact that the inclusions (LWAs) in these composites are by themselves heterogeneous, and contain multiple components (solid phase, PCM, water, and air) necessitate careful application of predictive models. Multi-step Mod-Tanaka mean-field homogenization methods, either based on known microstructural arrangement in the composite, or property contrast between the constituents, are applied to predict the composite thermal conductivity. A microstructural contrast factor is used to account for both the thermal conductivities and the volume fractions of the phases with the highest property contrast. Smaller contrast factors result in improved agreement of the models with the experiments, thereby aiding in the selection of suitable predictive schemes for effective properties of such multi-phase composites. (C) 2016 Elsevier Ltd. All rights reserved.