An aircraft cooling system including a cooler having a cold transfer circuit, in which a cold transfer medium circulates. The cooler supplies cooling energy to an aircraft device to be cooled. The aircraft cooling system further includes a heat transfer arrangement having a heat transfer circuit, in which a heat transfer medium circulates and which is thermally coupled to the cold transfer circuit of the cooler via a heat exchanger, in order to absorb waste heat generated by the cooler and transfer it to a cabin air extraction system. The heat transfer arrangement further includes at least one heat pump which brings about an increase of the heat energy transfer from the cold transfer medium circulating in the cold transfer circuit of the cooler to the heat transfer medium circulating in the heat transfer circuit, at least in certain operating phases of the aircraft cooling system.