The rotating electric machine (1) having a housing comprising first (14) and second (15) clamp members and an inner face, a stator comprising a stator body (41) clamped between the first and second clamp members and having an outer face extending opposite the inner face together defining an annular cooling chamber (21) surrounding the stator body, the stator body comprising a longitudinal stack of stator sheets (410), each stator pack of which comprises an annular core having an outer circumference and at least two radially centrifugal protuberances projecting from the outer circumference of the annular core, in the annular cooling chamber, and diametrically opposite one another, the stator sheets of the longitudinal stack being identical and two adjacent stator sheet of the longitudinal stack being angularly offset from each other such that the respective protuberances thereof do not extend opposite one another.