Cooling system for a rotary electric machine having an axis of rotation (A), comprising: a. a cooling jacket that is able to receive a stator of the rotary electric machine , b. a housing receiving the cooling jacket, wherein an outer wall of the cooling jacket forms, together with an inner wall of the housing, a cooling chamber that is able to be passed through by a cooling fluid, and wherein the housing comprises an inlet opening for the inlet of the cooling fluid into an inlet zone of the cooling chamber , and an outlet opening for the outlet of the cooling fluid from an outlet zone of the cooling chamber , the inlet opening and the outlet opening being formed in the housing , and wherein a separating element , which is separate from the cooling jacket and from the housing , is fixed to one of the outer wall of the cooling jacket and the inner wall of the housing in order to separate the inlet zone of the cooling chamber and the outlet zone of the cooling chamber , characterized in that the separating element comprises: a. a fixing part , with a first length , having a fixing face with a shape that is complementary to the shape of the one of the outer wall of the cooling jacket and the inner wall of the housing to which the separating element is fixed, b. a first separation part , with a second length , that is inclined with respect to the fixing part and not parallel to the fixing part , the first length being smaller than the second length such that the first separation part comprises a first free end which is not directly connected to the fixing part . a. a cooling jacket that is able to receive a stator of the rotary electric machine , b. a housing receiving the cooling jacket, wherein an outer wall of the cooling jacket forms, together with an inner wall of the housing, a cooling chamber that is able to be passed through by a cooling fluid, and wherein the housing comprises an inlet opening for the inlet of the cooling fluid into an inlet zone of the cooling chamber , and an outlet opening for the outlet of the cooling fluid from an outlet zone of the cooling chamber , the inlet opening and the outlet opening being formed in the housing , and wherein a separating element , which is separate from the cooling jacket and from the housing , is fixed to one of the outer wall of the cooling jacket and the inner wall of the housing in order to separate the inlet zone of the cooling chamber and the outlet zone of the cooling chamber , characterized in that the separating element comprises: a. a fixing part , with a first length , having a fixing face with a shape that is complementary to the shape of the one of the outer wall of the cooling jacket and the inner wall of the housing to which the separating element is fixed, b. a first separation part , with a second length , that is inclined with respect to the fixing part and not parallel to the fixing part , a. a fixing part , with a first length , having a fixing face with a shape that is complementary to the shape of the one of the outer wall of the cooling jacket and the inner wall of the housing to which the separating element is fixed, b. a first separation part , with a second length , that is inclined with respect to the fixing part and not parallel to the fixing part , the first length being smaller than the second length such that the first separation part comprises a first free end which is not directly connected to the fixing part . <EOS>