A method and a device for operating a drive train of a motor vehicle are provided. The drive train includes at least a first and a second shaft, a first clutch having at least one first friction surface pairing, and an electric drive, the first and the second shaft being coupleable to one another via the at least one first friction surface pairing, wherein for cooling the first clutch, a fluid is used via which a drag torque of the first clutch is influenced after the first clutch is disengaged, the method including: a) Rotating the first shaft and the second shaft when the first clutch is at least partially engaged; b) Disengaging the first clutch; c) Accelerating the first shaft by means of the electric drive and discharging the fluid from an area of the at least one first friction surface pairing; wherein the drag torque of the first clutch is reduced by the accelerated discharge of the fluid.