Evaporate thermal management systems for and methods of grazing incidence collectors (GICs) for extreme ultraviolet (EUV) lithography include a GIC shell interfaced with a jacket to form a structure having a leading end and that defines a chamber. The chamber operably supports at least one wicking layer. A conduit connects the wicking layer to a condenser system that support cooling fluid in a reservoir. When heat is applied to the leading end, the cooling fluid is drawn into the chamber from the condenser unit via capillary action in the wicking layer and an optional gravity assist, while vapor is drawn in the opposite direction from the chamber to the condenser unit. Heat is removed from the condensed vapor at the condenser unit, thereby cooling the GIC mirror shell.