The fast volumetric deposition of multi-MeV high current runaway electron (RE) beams constitutes the most critical issue for the ITER tungsten (W) first wall (FW) longevity. Such relativistic electron beams could generate extreme volumetric power densities inside the FW armor which lead to significant vaporization, deep melting and even material explosions, as well as to elevated temperatures at the bond interface with the cooling substrate that could cause rupture and water leaks. Here the thermal response of the ITER FW is modeled with a three-stage, one-way coupled workflow focusing on assessments of the extent of the wall damage and the increase of the bond interface temperature for varying W thickness. Increased W thickness is found to be essential for wall protection against intense RE dissipation events in terms of both W tile damage and cooling system integrity.