Vehicular transmission stop control system

A vehicular transmission comprises an engine E, a continuously variable transmission CVT and a starting clutch 5. The driving force from the engine E is conveyed through the continuously variable transmission CVT with a speed change to a countershaft 2, and the starting clutch 5 is used to convey this driving force from the countershaft 2 to wheels of a vehicle. The continuously variable transmission CVT is hydraulically controlled by a control valve CV which receives control signals through a line 35 from an electrical control unit ECU. When the temperature of the oil used for engaging and disengaging the starting clutch 5 is equal to or higher than a predetermined temperature, the transmission allows the engine E to stop operating. This control to terminate the operation of the engine is an idling elimination control and is achieved by terminating the fuel supply to the engine and by maintaining the resulting condition of non-fuel supply while the vehicle is being decelerated and brought into a halt.