In a cooling system of an aircraft turbojet engine surrounded by a nacelle, a heat-transfer fluid is circulated that is less flammable than a lubricant (H) for the turbojet engine and liquid at temperatures between −70° C. and +175° C., the heat-transfer fluid (C) being intended to circulate in a closed-circuit circulation duct including a first surface heat-exchanger between the heat-transfer fluid (C) and air (F), at the level of at least one of the outer fairing and the inner fairing of the nacelle, and a second surface heat-exchanger between the heat-transfer fluid (C) and the lubricant (H).