The turbine vane segment includes inner and outer walls with a vane extending therebetween. The vane includes leading and trailing edge cavities and intermediate cavities. An impingement plate is spaced from the outer wall to impingement-cool the outer wall. Post-impingement cooling air flows through holes in the outer wall to form a thin air-cooling film along the outer wall. Cooling air is supplied an insert sleeve with openings in the leading edge cavity for impingement-cooling the leading edge. Holes through the leading edge afford thin-film cooling about the leading edge. Cooling air is provided the trailing edge cavity and passes through holes in the side walls of the vane for thin-film cooling of the trailing edge. Steam flows through a pair of intermediate cavities for impingement-cooling of the side walls. Post-impingement steam flows to the inner wall for impingement-cooling of the inner wall and returns the post-impingement cooling steam through inserts in other intermediate cavities for impingement-cooling the side walls of the vane.