The ability to tune diverse electronic phases in strongly correlated complex oxides offers a fertile platform for exploring a wide range of phenomena, such as unconventional superconductivity in cuprates and Mott physics in vanadates and nickelates. In particular, the observed memristive behavior in the superconducting cuprate YBa2Cu3O7-δ highlights the potential of this class of oxides for multilevel memories and as building blocks in neuromorphic devices . Bi2Sr2CaCu2O8+δ (BSCCO) belongs to the cuprate family and exhibits strong crystalline anisotropy due to their intrinsic multilayer structure composed of alternating conducting (CuO2) and insulating layers (which act as charge reservoirs) along the crystalline c-axis of the material. A consequence of this pronounced large anisotropy, is the possibility to mechanically exfoliate BSCCO single crystals into thin flakes, in a similar way as with other van der Waals (vdW) materials . In this work, we investigate the memristive behavior of BSCCO flakes in a crossbar structure which exhibits non-volatility, long retention times (~3 hours) and large endurance (over 1000 cycles). Non-volatile switching is observed over a temperature range from 60 K up to room temperature. A resistance window exceeding one order of magnitude is observed at high temperatures. Multiple resistance states can be accessed by tunning the partial reset voltage. A compact behavioral model is shown to reproduce both the hysteron and the complete I(V) loops at all temperatures. These findings demonstrate the potential of BSCCO for cryogenic memory applications and 2D electronic devices.