Liquid-cooling device for an internal combustion engine, having - a main circuit comprising the water chamber of the engine; - an auxiliary circuit linked to the main circuit, said auxiliary circuit comprising a storage tank for storing a coolant for an internal combustion engine; said storage tank being connected to the cooling device and comprising ∘ a heat-insulated rigid tank; ∘ a deformable bladder; ∘ a cavity formed by the interior of the bladder; and ∘ a cavity formed between the bladder and the rigid tank; ∘ a plurality of connection orifices (15 and 16) intended to be connected to said auxiliary circuit; - pumping means (21, 22, 23) controlled by control means, - characterized in that the pumping means are able: - when the engine is stopped, to transfer the coolant heated by the motor from the main circuit to a first of the two cavities (17, 18) of the storage tank and the coolant at ambient temperature from the second of the two cavities (17, 18) of the storage tank to the main circuit; - before the engine is started, to transfer the coolant at ambient temperature from the main circuit to the second of the two cavities (17, 18) and the coolant from the first of the two cavities (17, 18), stored in order to heat the main circuit, to the main circuit so as to accelerate the heating of the engine during starting. - a main circuit comprising the water chamber of the engine; - an auxiliary circuit linked to the main circuit, said auxiliary circuit comprising a storage tank for storing a coolant for an internal combustion engine; said storage tank being connected to the cooling device and comprising ∘ a heat-insulated rigid tank; ∘ a deformable bladder; ∘ a cavity formed by the interior of the bladder; and ∘ a cavity formed between the bladder and the rigid tank; ∘ a plurality of connection orifices (15 and 16) intended to be connected to said auxiliary circuit; ∘ a heat-insulated rigid tank; ∘ a deformable bladder; ∘ a cavity formed by the interior of the bladder; and ∘ a cavity formed between the bladder and the rigid tank; ∘ a plurality of connection orifices (15 and 16) intended to be connected to said auxiliary circuit; - pumping means (21, 22, 23) controlled by control means, - characterized in that the pumping means are able: - when the engine is stopped, to transfer the coolant heated by the motor from the main circuit to a first of the two cavities (17, 18) of the storage tank and the coolant at ambient temperature from the second of the two cavities (17, 18) of the storage tank to the main circuit; - before the engine is started, to transfer the coolant at ambient temperature from the main circuit to the second of the two cavities (17, 18) and the coolant from the first of the two cavities (17, 18), stored in order to heat the main circuit, to the main circuit so as to accelerate the heating of the engine during starting. - when the engine is stopped, to transfer the coolant heated by the motor from the main circuit to a first of the two cavities (17, 18) of the storage tank and the coolant at ambient temperature from the second of the two cavities (17, 18) of the storage tank to the main circuit; - before the engine is started, to transfer the coolant at ambient temperature from the main circuit to the second of the two cavities (17, 18) and the coolant from the first of the two cavities (17, 18), stored in order to heat the main circuit, to the main circuit so as to accelerate the heating of the engine during starting.