A method for controlling a coolant pump for an engine includes delivering a coolant via a coolant pump impeller into a delivery duct to a pump outlet, and adjusting the delivery based on a position of an adjustable control slide which controls a throughflow cross-section of an annular gap between the coolant pump impeller outlet and the delivery duct. A first pressure chamber on a side of the control slide is filled with a pressurized coolant to decrease the throughflow cross-section and the coolant volume flow delivered to the pump outlet, or a second pressure space arranged on an opposite side is filled with the pressurized coolant to increase the throughflow cross-section and the coolant volume flow delivered to the pump outlet. The control slide is moved into a defined position when the engine is switched off dependent on a coolant temperature and remains in that position until a restart.