In order to provide an automatically operating cooling air regulating device for a grate cooler for cooling hot bulk material such as cement clinker, for example, which can be constructed easily and can be used without problems both for non-moving and also in particular for moving cooling grate regions or moving cooling grate systems, a regulating device with a regulator housing which is arranged below the cooling grate, performs its movements with it and is flowed through by the cooling air supplied is proposed according to the invention, an inner body which can be moved translatorily by the cooling air flow being guided displaceably in the regulator housing and the free flow cross section of the regulator housing remaining for the cooling air being reduced automatically with increasing height inside the regulator housing of the inner body against which the cooling air flows, and vice versa.