A controllable cooling system for a motor vehicle, comprising: a coolant circuit for supplying and discharging coolant to and from an internal combustion engine of the vehicle; a mechanically operated, controllable main coolant pump comprising an inlet for supplying the coolant into the main coolant pump and an outlet for discharging the coolant to the internal combustion engine, and an electrically operated, controllable secondary coolant pump comprising an inlet for supplying the coolant into the secondary coolant pump and an outlet for discharging a coolant, conveyed as a bypass coolant flow, towards the main coolant pump, wherein the secondary coolant pump is arranged upstream of the main coolant pump in the direction of flow, branching off from a coolant line leading to the main coolant pump in the direction of coolant flow, the coolant conveyed by means of the secondary coolant pump is supplied, downstream of the main coolant pump and without flowing through the main coolant pump, into the outlet leading to the internal combustion engine, the secondary coolant pump comprises a pump casing with a pump chamber formed therein, wherein on a section of the pump casing an electric motor is arranged which provides driving power for the secondary coolant pump by means of a drive shaft extending into the pump chamber, the secondary coolant pump in the pump chamber comprises an impeller serving as a conveyor member which is coaxially arranged on the drive shaft and drivably connected thereto, and the secondary coolant pump comprises a control slide valve formed on the impeller which can be moved at least to open and closed positions, for controlling the bypass coolant flow conveyed by the secondary coolant pump, particularly for preventing back-flow of the coolant in a direction opposite to the conveying direction of the secondary coolant pump. a coolant circuit for supplying and discharging coolant to and from an internal combustion engine of the vehicle; a mechanically operated, controllable main coolant pump comprising an inlet for supplying the coolant into the main coolant pump and an outlet for discharging the coolant to the internal combustion engine, and an electrically operated, controllable secondary coolant pump comprising an inlet for supplying the coolant into the secondary coolant pump and an outlet for discharging a coolant, conveyed as a bypass coolant flow, towards the main coolant pump, wherein the secondary coolant pump is arranged upstream of the main coolant pump in the direction of flow, branching off from a coolant line leading to the main coolant pump in the direction of coolant flow, the coolant conveyed by means of the secondary coolant pump is supplied, downstream of the main coolant pump and without flowing through the main coolant pump, into the outlet leading to the internal combustion engine, the secondary coolant pump comprises a pump casing with a pump chamber formed therein, wherein on a section of the pump casing an electric motor is arranged which provides driving power for the secondary coolant pump by means of a drive shaft extending into the pump chamber, the secondary coolant pump in the pump chamber comprises an impeller serving as a conveyor member which is coaxially arranged on the drive shaft and drivably connected thereto, and the secondary coolant pump comprises a control slide valve formed on the impeller which can be moved at least to open and closed positions, for controlling the bypass coolant flow conveyed by the secondary coolant pump, particularly for preventing back-flow of the coolant in a direction opposite to the conveying direction of the secondary coolant pump. the secondary coolant pump is arranged upstream of the main coolant pump in the direction of flow, branching off from a coolant line leading to the main coolant pump in the direction of coolant flow, the coolant conveyed by means of the secondary coolant pump is supplied, downstream of the main coolant pump and without flowing through the main coolant pump, into the outlet leading to the internal combustion engine, the secondary coolant pump comprises a pump casing with a pump chamber formed therein, wherein on a section of the pump casing an electric motor is arranged which provides driving power for the secondary coolant pump by means of a drive shaft extending into the pump chamber, the secondary coolant pump in the pump chamber comprises an impeller serving as a conveyor member which is coaxially arranged on the drive shaft and drivably connected thereto, and the secondary coolant pump comprises a control slide valve formed on the impeller which can be moved at least to open and closed positions, for controlling the bypass coolant flow conveyed by the secondary coolant pump, particularly for preventing back-flow of the coolant in a direction opposite to the conveying direction of the secondary coolant pump.