A hydraulic system for controlling a belt-driven conical-pulley transmission. A pump draws a working medium from a working medium tank or through a cooler return valve from a cooler return line. The cooler return valve is a minimum pressure valve that holds closed a connection between the cooler return line and a pump inlet line through the cooler return valve, as long as the pressure in the cooler return line remains below a specified minimum pressure. The cooler return valve also opens the connection between the cooler return line and the pump inlet line through the cooler return valve as soon as the specified minimum pressure in the cooler return line is exceeded.