The authors present a multiple-relaxation-time lattice Boltzmann model with an off-diagonal collision matrix for use in predicting the thermal conductivity of anisotropic heterogeneous materials with anisotropic components. Model accuracy was first confirmed through comparison with previous simulation results. In this paper the model was applied to measure the tranverse and longitudinal thermal conductivities of 3D4D braided composites. The TPS method was used to measure the conductivities experimentally for comparison ...