containing steel used for conventional high pressure turbine shaft an annular groove 11 having dimensions and configurations as shown in fig2 a was in the same manner as described with respect to fig1 machined and formed in the shaft material a partitioning wall 12 was inserted in the annular groove 11 and thereafter a heat insulating material 13 was filled therein the shaft thus assembled was disposed in an electric furnace and the section l on the low pressure side and the section h on the high pressure side were heated to temperatures of 915 u00b0 c and 960 u00b0 c respectively after heating the low pressure section l was treated by water spray quenching whereas the high pressure section h was cooled by air blast during the cooling stages the temperatures of peripheral portion and central portions of the shaft were measured the measured temperatures are shown in fig2 b where s and k denote the temperatures of the peripheral and the central portions being disposed in an electric furnance respectively and c denotes the cooling speed as is apparent from the graphs of fig2 b it may be seen that although there was some transition region in the temperature distribution during heating in the electric furnace a generally desirable temperature profile was obtained at a position about 500 mm from the center of annular groove 11 in either direction due to the effects of the groove 11 and the heat insulative material 13 also though there was a transition region with respect to the cooling speed c of the central portion in comparison with the high pressure section h a sufficiently high cooling speed was obtained in the low pressure section l quenching and tempering according to the invention were carried out and thereafter test segments of material.