The invention relates to the control of air flows for cooling the axial walls of a high-temperature combustion chamber in which the walls are provided with through holes forming multiple perforations, and involves arranging the multiple perforations so that the cooling airflow permeability of the walls in the downstream zone of the chamber decreases in the downstream direction in order to compensate for the effects of the increase in pressure drop due to variation of the gas flow velocity. The invention is particularly applicable to sharply convergent combustion chambers such as twin-head combustion chambers.