We report temperature dependent electrical characteristics of two-terminal Ag/a-COx/ta-C/Pt memristors. In these asymmetric devices, defects at the Ag/a-COx interface are passivated by oxygen. This alleviates Fermi level pinning and hence increases the height of the Schottky barrier formed at the interface. Electric-field-induced detrapping of electrons from sp2-related defects in the ta-C causes the observed resistive switching. This occurs entirely in the insulating regime, i.e., with conductance ≪ 2e2/h, enabling ultralow power resistive switching (∼6 nW). Nonlinear temperature dependent ON/OFF ratios and short-term memory characteristics (governed by thermal detrapping kinetics) suggest suitability for temporal neuromorphic computing and sensing applications.