The thermal performance of the first wall (FW) monoblock module, made from carbon fiber composite (CFC) or tungsten alloy with a castellated plasma phasing surface, was analyzed for runaway electron (RE) impact under reactor conditions. A water cooling system with Cu pipes embedded into the module is used. Calculations demonstrate that, in ITER, for an expected RE pulse duration [approximately]0.1sec and deposition energy of [approximately]30MJ/m2 , the heat generation in a W monoblock occurs within a thin surface layer ([approximately]10m) which, however, does not melt. In the CFC case, heat generation occurs deep in the bulk ([approximately]1000m), but CFC does not experience brittle destruction. The intense X-ray radiation caused by runaways is strongly attenuated within a 10-mm-thick layer of W and does not pose any threat for the cooling system. For the CFC case, a small but significant heat generation caused by the RE can occur in the Cu pipe.