Abstract: A cooled wall structure including a hot side, a cold side, a linear slot opening through the hot side, a plurality of diffusion chambers below the hot side separated therefrom by relatively thin bridge sections of the wall structure and arrayed in checkerboard fashion on opposite sides of the linear slot and opening into the linear slot through the sidewalls thereof, and a plurality of passages from the cold side to each of the diffusion chambers. The cold side is exposed to coolant gas under pressure and the passages are aimed at the bridge sections so that jet of cooling gas issuing from the passages impinge against the bridge section for convection cooling the hot side. The bridge sections prevent direct penetration of the coolant gas jets into the environment adjacent the hot side. The coolant gas flows from the diffusion chambers into the linear slots and from the linear slots over the hot side to form on the latter a coolant film or blanket.