The invention relates to a method of regulating the temperature of a heat regenerator (ST1, ST2) used in an installation (10) for storing energy by adiabatic compression of air. The regenerator is subjected to successive operating cycles, each cycle comprising a compression stage followed by an expansion stage. Between two successive cycles, the method consists in cooling a bottom compartment (26a) of the layer of refractory material (26) of the regenerator that is situated in the proximity of the bottom distribution box (24) in order to bring the air leaving the heat regenerator to a temperature that is compatible with the range of temperatures required during the compression stages. The invention also provides such a heat regenerator.