Ceramic matrix composites (CMC) are very attractive materials for structural applications at high temperatures. Not only must CMC be damage tolerant, but they must also allow thermal management. For this purpose heat transfers must be controlled even in the presence of damage. Damage consists in multiple cracks that form in the matrix and ultimately in the fibers, when the stresses exceed the proportional limit. Therefore the thermal conductivity dependence on applied load is a factor of primary importance for the design of CMC components. This original approach combines a model of matrix cracking with a model of heat transfer through an elementary cracked volume element containing matrix crack and an interfacial crack. It was applied to 1D composites subject to tensile ant thermal loading parallel to fiber direction in a previous paper. The present paper compares predictions to experimental results.