Quenched layers are formed without irregularities on the inner circumferential surface of a track bushing having a small inside diameter or on the inner circumferential surfaces of two or more track bushings which are subjected to quenching in an overlapped condition. To introduce a cooling medium for cooling the inner circumferential surface of the track bushing, a guide tube having an outside diameter smaller than the inside diameter of the track bushing is disposed on the side of the inner circumferential surface and the cooling medium introduced by the guide tube is diverted by a diverting member having a spherical or similar curved surface, such that the cooling medium is allowed to flow in a direction substantially parallel with an axial direction of the track bushing 1 within a space defined by the outer circumferential surface of the guide tube and the inner circumferential surface of the track bushing, thereby performing laminar flow cooling.