In some conventional fan revolution speed control methods, variable control of the number of revolutions of a cooling fan is performed by a process comprising steps of detecting an actual temperature of cooling target fluid, i.e. fluid to be cooled by the cooling fan, such as hydraulic oil and circulating radiator cooling water for cooling an engine (such cooling water is hereinafter referred to as coolant), determining a target fan revolution speed by a system of a proportional integral control unit based on the difference between the actual temperature detected and a target temperature, and changing the fan revolution speed based on the target fan revolution speed so as to bring the actual temperature of the cooling target fluid down to the target temperature.  One example of such control methods is disclosed in Japanese Patent Publication No.  3295650. 
During a normal course of operation, such a conventional fan revolution speed control method that calls for calculating a fan revolution speed by a system of a proportional integral control unit and changing the fan revolution speed so as to bring the actual temperature down to the target temperature presents no problem.  However, as shown in FIG.  7, such a conventional method is prone to delay in rise of fan revolution speed in response to an initiation command.  For example, in cases where the target temperature is 60° C., the fan revolution speed, which is shown by a two-dot chain line, does not rise immediately when the actual temperature of the cooling target fluid exceeds the target temperature of 60° C. but after the cooling target fluid greatly overshoots the target temperature.  As shown in FIG.  7, the fan revolution speed may not rise until the actual temperature of the hydraulic oil, which is a cooling target fluid, at the pump suction section of a hydraulic pump exceeds 70° C., or, until the actual temperature of the coolant, which is another cooling target fluid, approaches 90° C. at the intake section of the radiator. 
The aforementioned delay in rise of fan revolution speed is caused by accumulation of negative integral elements when performing integration by the proportional integral control unit. 
In order to solve the above problems, an object of the invention is to provide a fan revolution speed control method that prevents delay in rise of fan revolution speed and thereby safeguards against the actual temperature overshooting the target temperature, which would otherwise cause unnecessary increase in the fan revolution speed.