A cooling system of the invention mounted on a motor vehicle has a damper configured to switch over an air blow mode between an inside air intake mode of taking in the air from a passenger compartment of the motor vehicle via operation of a battery blower fan and directly blowing the intake air to a battery and an A/C intake mode of taking in the air cooled down by an air conditioner (evaporator) via operation of the battery blower fan and blowing the cooled intake air to the battery. In response to a switchover demand of the air blow mode, when a vehicle speed is not lower than a preset reference speed, a switchover of the damper is immediately performed to switch over the air blow mode. When the vehicle speed is lower than the preset reference speed, the switchover of the damper is prohibited to keep the air blow mode unchanged. At the higher vehicle speed, the drive-related noise (background noise) sufficiently masks the wind noise occurring in the course of the switchover of the damper. The damper is thus switched over only at the vehicle speed of not lower than the preset reference speed. This arrangement effectively prevents the driver and the other passengers from feeling odd and uncomfortable.