Heat shield with a support structure and method for cooling the support structure

The shield (15) has heat shield bricks fastened to a supporting structure (16) when a cooling air groove is partially covered along a longitudinal direction (7). A channel-shaped groove section (8) is formed into which a cooling air duct (9) opens, where cooling air flowing out of the cooling air duct is deflected along the longitudinal direction of the cooling air duct. Brick holders (2a, 2b) comprise a holding section (3) that is fastened to the heat shield bricks, and a fastening section (4), which is fastened to the supporting structure. An independent claim is also included for a method for cooling a support structure of a heat shield.