Monte Carlo (MC) modeling has proven to be an accurate and efficient technique to deal with many physics, chemistry and engineering problems. It has successfully adapted to solve the Boltzmann Transport Equation for phonons. In the latter case, heat propagation in nanostructured materials like nanofilms, nanowires or phononic crystals can be addressed accurately. With this technique, thermal conductivity, Kapitza resistance and thermal conductance can be appraised as long as phonon dispersions and relaxation times are known. This is the case for major semiconducting materials but becomes no longer true with complex compounds where such data are unavailable or partial. To answer this challenge we propose a new multiscale approach which joins DFT calculations to MC modeling. Using ab-initio techniques accurate material bulk phonon properties can be appraised. They are the input of an improved MC tool which is used to model the thermal properties of nanostructures made of complex compounds.