A turbine engine wall having a cold side and a hot side and including a plurality of cooling orifices for enabling air flowing on the cold side of the wall to penetrate to the hot side at least some of the cooling orifices being plugged by a plugging material so as to define a minimum level of porosity for the wall corresponding to putting the turbine engine into service, and the plugged cooling orifices being suitable for being unplugged progressively throughout the lifetime of the turbine engine in order to define a maximum level of porosity for the wall corresponding to an end of lifetime for the turbine engine, the plugging being performed by alternating at least one of the following rows or lines: circumferential rows, axial rows, diagonal lines, so as to lie in the range one-third to one-half of the maximum porosity.