Abstract: A lubricant is supplied to a bearing for a rotary shaft by an oil pump capable of discharging the lubricant at different flow rates depending upon its speed of operation. The oil pump is preliminarily operated to allow the user to derive and determine a relationship between temperature rise in the bearing and the flow rate of the lubricant by the oil pump with rate of rotation of the shaft as parameter. An optimum flow rate at which the temperature rise is minimized can be determined from such a relationship. The oil pump is operated such that the lubricant is discharged at this optimum flow rate and according to the current rotary speed of the shaft. Corresponding to different rotary speeds of the shaft, a temperature characteristic curve representing these optimum flow rates of the lubricant can be obtained, and this temperature characteristic curve may be used to vary the speed of operation of the oil pump to change the flow rate of the lubricant according to different rotary speeds of the shaft.