A device for rectifying the current of a rotary electric machine comprising a bearing (50) with through openings (51) for a coolant, that comprises at least one module (100) including a holder (10, 16) for holding current rectifying members (93, 94) having the same phase as the machine, said holder (10, 16) including a heat sink (16) with vanes (18) at least partially covering an opening (51) in the bearing (50). A rotary electric machine including such a current rectifying device. Application: alternators of automotive vehicles with internal ventilation.