The invention relates to a method for cooling a heat shield element (13), comprising a wall (15) with an inner side (151) and an outer side (153), which can be exposed to a hot fluid, and wherein a coolant (K) is introduced into an impingement region (17) of that heat shield element (13) and an impingement flow (19) of said coolant (K) is directed on a surface area (23) of that inner side (151) through a plurality of impingement holes (21), effecting an impingement pressure drop (ΔP I ). In the method discharge flow (25) is metered through a number of discharge holes (27) through said wall (15) from the inner side (151) to the outer side (153) of the wall (15), effecting a discharge pressure drop (ΔP D ) in series with the impingement pressure drop (ΔP I ). The impingement pressure drop (ΔP I ) and the discharge pressure drop (ΔP D ) are matched to one another so that a required coolant flow (K) is generated which yields a predetermined heat-transfer coefficient of the wall (α).