The lifetime of the divertor in tokamak nuclear fusion reactors is uncertain, due to the severe heat, ion and neutron loads that are imposed on the plasma-facing monoblocks, which are made of tungsten. In this work, the microstructural evolution throughout the monoblock is modelled, using a multi-scale model that spans from displacement damage evolution to macroscopic material properties and temperature profiles. The evolution of the hardness and the thermal conductivity as a function of monoblock depth are studied, under a combination of heat and neutron loading, based on the concentrations of the radiation-induced defects. An increase of the temperature gradient over the monoblock is predicted, which entails serious consequences for the m...