A WSe2-based vertical graphene-transition metal dichalcogenide heterojunction barristor shows an unprecedented on-current increase with decreasing temperature and an extremely high on/off-current ratio of 5 x 10(7) at 180 K (3 x 10(4) at room temperature). These features originate from a trap-assisted tunneling process involving WSe2 defect states aligned near the graphene Dirac point.