An inking unit for a printing machine includes one or more distributor drums, ink transfer rollers, ink application rollers, an ink reservoir for printing ink and an ink metering device having at least one electrically controllable valve for metering the printing ink. In accordance with the invention, there are provided a high-pressure pumping device for supplying the ink metering device with printing ink at a predetermined high pressure from the ink reservoir, and a heating device for heating the printing ink to a predetermined temperature above room temperature. Moreover, the at least one valve of the ink metering device has a short reaction time and a flow rate with a low dependence upon viscosity. The invention also relates to a method for supplying printing ink to a printing machine.