Dual clutch transmission system, vehicle and method of cooling. A dual clutch transmission system, including coaxial first and second engageable and disengageable torque transmitting assemblies, configured to be installed in a power train of a vehicle, the system including a main flow path for supply of cooling fluid, wherein the main flow path branches into a first flow path for supply of cooling fluid to the first torque transmitting assembly, and a second flow path for supply of cooling fluid to the second torque transmitting assembly, wherein the system includes a third flow path for supplying cooling fluid, which is discharged from the second torque transmitting assembly, to the first torque transmitting assembly, the third flow path preferably being arranged within a space defined by a housing of the dual clutch transmission system.