An electric starter-generator is described. The generator may comprise a rotor, a housing, two bearings, a stator, and a cooling-fluid flowpath. The cooling-fluid flowpath may comprise a cooling-fluid entrance and exit, and a cooling-fluid channel in fluid communication with the entrance and exit. At least a portion of the channel may be defined by a fluid-tight coupling of the housing and a sleeve radially surrounding the outer race of either the bearings. The portion may form an annulus about the axis. The portion may comprise a radially inner surface defined by the sleeve, a radially outer surface define by said housing, and two axial surfaces. The two axial surfaces may extend a distance from the radially inner to outer surfaces that is less than a distance from one of the two axial surfaces to the other of the two axial surfaces.