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 magnitude of the thermal stresses and the accompanying surface temperature. For the selected parameter set, the high surface temperature leads to recrystallization of a small layer of material near the surface, locally reducing the amount of irradiation hardening. Interim heat treatments of 1 h are simulated, which evoke recrystallization in the monoblock and which either reset the accumulated irradiation hardening, or keep it low, throughout the monoblock, thereby increasing the ductility again, and proving that such treatments could be a valuable tool on the way to prolongation of the lifetime of these monoblocks.