a first embodiment of the invention is discussed immediately below with reference to fig1 a schematic of the first embodiment . in this embodiment , a cooling apparatus for a liquid - cooled internal combustion engine is used to cool an automobile engine . in fig1 numeral 10 designates a liquid - cooled internal combustion engine ( engine ), numeral 20 designates a radiator that cools a coolant that has been : discharged from the engine 10 and returns the cooled coolant to the engine 10 , and numeral 21 designates a cooling fan for supplying cold air to the radiator 20 . numeral 30 designates a bypass passage through which coolant discharged from the engine 10 bypasses the radiator 20 and returns to the engine 10 ; numeral 40 designates an electronic flow rate control valve ad ( referred to as the first valve ) that controls the flow rates through both the radiator 20 and the bypass passage 30 ; numeral 50 designates a coolant pump that is driven by the engine 10 . numeral 60 designates a heat exchanger ( heater ) that heats air to be discharged into a vehicle compartment by using the coolant ( engine waste heat ) as a heat source ; numeral 70 designates an electromagnetic valve ( referred to as the second valve ) that opens and closes a passage through which the coolant is supplied to the heater 60 ; numeral 61 designates an air conditioning fan , which discharges cooled air into the vehicle compartment . numeral 80 designates a torque converter ( fluid coupling ) for an automatic transmission ; and numeral 90 designates an oil cooler ( oil heat exchanger ) that exchanges heat between the working oil of the torque converter 80 ( automatic transmission fluid or atf ) and the coolant . numeral 101 designates a first coolant temperature sensor that is mounted within the bypass passage 30 adjacent the first valve 40 and numeral 102 designates a second coolant temperature sensor that is mounted adjacent the inlet port of the pump 50 to sense the temperature of the coolant returned to the engine 10 . numeral 103 designates a pressure sensor that senses the suction negative pressure of the engine 10 ; numeral 104 designates an engine speed sensor , which measures the speed of the engine 100 , and numeral 105 designates an ambient temperature sensor which measures the temperature of the ambient air . signals from the sensors 101 through 105 and an on / off signal from a start switch 106 of the vehicle &# 39 ; s air conditioner are input to an electronic control unit ( ecu ) 100 , which controls the first and second valves 40 and 70 and the cooling fan 20 in accordance with predetermined programs . the operations of the first and second valves 40 and 70 are discussed immediately below with reference to both the flow chart shown in fig2 and the schematic shown in fig1 . when the engine 10 starts after the vehicle &# 39 ; s ignition switch ( not shown ) is turned on , the outputs of the speed sensor 104 , the pressure sensor 103 , the first and second coolant temperature sensors 101 and 102 , the ambient temperature sensor 105 , and the start switch 106 are read by the ecu 100 , as depicted by step s 100 in fig2 . the ecu 100 then calculates , the engine load using the engine speed and the suction negative pressure . based on the engine load thus obtained , the target temperature of the coolant ( referred to as the target temperature tmap ), the flow rate of the coolant to be returned to the engine 10 , and the temperature of the coolant to be returned to the engine at which warm - up is deemed complete ( referred to as the warm - up completion temperature tw 1 ) are determined from a map ( not shown ) ( s 110 ). the temperature of the coolant flowing through the bypass passage 30 ( referred to as the bypass coolant temperature tb ), which is measured by the first temperature sensor 101 , is compared with the warm - up completion temperature tw 1 , which would be 100 ° c . of the coolant were pure water ( s 120 ). if the bypass coolant temperature tb is less than the warm - up completion temperature tw 1 , the engine load ( as measured by the pressure sensor 103 ) is compared with a predetermined value r 0 ( s 130 ). if the measured engine load is less than the predetermined value r 0 , the second valve 70 is closed to prevent coolant from flowing to the oil cooler 90 and the warm - up control mode operation in which the coolant is circulated at least between the engine 10 and the bypass passage 30 . in the warm - up control mode , the first valve 40 limits the coolant flow through the engine 10 to between 1 and 5 l / min , which range is narrower than the conventional range of ( 10 to 15 l / min ) ( s 140 , s 150 ). if the measured bypass coolant temperature tb is greater than the warm - up completion temperature tw 1 , so that warm - up is deemed completed , or if the engine load is greater than the predetermined value r 0 , so that the warm - up control mode operation is no longer necessary , the second valve 70 is opened to allow the coolant to flow through the oil cooler 90 . a high temperature control mode operation is the coolant temperature , as measured by the second coolant temperature sensor 103 , is limited to the range 95 to 110 ° c . ( s 160 , s 170 ). for low coolant temperatures , 1 to 5 l / min of coolant flows through the engine 10 , which is sufficient to prevent local boiling of coolant in the engine 10 . fig8 shows the empirical relationship between the coolant flow rate in the warm - up control mode and the time needed to warm - up a 2000 cc ( displacement ) engine . when the coolant flow rate is 1 l / min , engine warm - up requires approximately 88 % of the time required when the coolant flow rate is 15 l / min ; when the coolant flow rate is 5 l / min engine warm - up requires approximately 98 % of the time required when the coolant flow rate is 15 l / min . thus , the time required to warm - up the engine decreases with coolant flow rate for flow rates less than 5 l / min . such low flow rates are , however , sufficient to prevent heat - induced deformation of the engine 10 ( cylinder head , cylinder block , etc .) moreover , when the coolant temperature is less than the warm - up completion temperature tw 1 , the coolant is allowed to flow through the oil cooler 90 . since the temperature of the coolant does not decrease due to heat transfer from the coolant to the atf , the time required to warm - up the engine is further shortened . fig3 a shows the empirical variation of the coolant temperature at the outlet of the engine and the oil temperature at the outlet of the oil cooler . in fig3 a , “ a ” represents the conventional cooling apparatus shown in fig4 “ b ” represents the conventional cooling apparatus shown in fig5 and “ c ” represents the cooling apparatus according to the first embodiment of the present invention . fig4 depicts a conventional in which the first valve 40 is replaced with a thermostat that controls the opening of a flow control valve that utilizes the volume change of a wax material . fig5 depicts a conventional cooling apparatus in which the oil cooler 90 is mounted in the radiator 20 . fig3 a shows that the temperature of coolant discharged from the engine quickly reaches 80 ° c ., the temperature at which the fuel injection control mode is switched from a start control mode to a normal control mode . fig3 b depicts the time dependence of the vehicle speed when the coolant temperature evolves as shown in fig3 a . since coolant flows through the oil cooler 90 only when the coolant temperature exceeds the warm - up completion temperature tw 1 , high - temperature coolant may be used to heat the atf when the temperature of the atf is low . therefore , not only can the engine be warmed - up more quickly , but the fuel consumption of the vehicle can also be improved by using the high - temperature coolant to warm the atf thereby reduce the friction loss . in this embodiment , coolant flows through the oil cooler 90 only when the coolant temperature exceeds 100 ° c . and , hence , the temperature difference between the atf and the coolant can be increased . consequently , the temperature of the atf can be rapidly increased , as shown by fig3 a . after the engine is warmed - up , engine coolant temperature is maintained between 95 ° c . and 110 ° c . and , hence , the fuel consumption can be improved by increasing the temperature of the lubricant ( engine oil ) to thereby reduce the friction loss , as may be seen in fig6 . in fig6 “ a ” represents the conventional cooling apparatus shown in fig4 ; “ b ” represents to the conventional cooling apparatus shown in fig5 ; and “ c ” represents the cooling apparatus according to the first embodiment of the present invention . a second embodiment of the present invention will be discussed below . in the second embodiment shown in fig7 the first valve 40 and the second valve 70 are replaced with a single valve 45 . the present invention can readily be modified as follows . in the first and second embodiments , the temperature of the coolant that flows through the oil cooler 90 was taken to be the same as the temperature at which engine warm - up is deemed complete . however , these two temperatures may be allowed to differ . moreover , although an oil cooler that exchanges heat between the atf and the coolant is used in the first and second embodiments , an oil cooler that exchanges heat between the engine oil and the coolant can also be used . furthermore , although the coolant pump 50 driven by the engine 10 is used in the first and second embodiments , a coolant pump driven by an electric motor can also be used .