Cryogenic memristors based on the high-temperature superconductor YBa₂CuO_7-δ offer significant potential as nonvolatile memory elements or unit cell for analog artificial neural networks for future applications such as control units for quantum processors, cryogenic data centers or space-related electronics. In this work, the experimental switching capabilities of cuprate-based memristors are analyzed in terms of the material-specific physics. This work investigates the experimental switching behavior of cuprate-based memristors across temperatures from cryogenic to room temperature. The underlying interpretation, namely the trapping of injected charge carriers at a metal interface and field-induced detrapping, is incorporated into a physically inspired compact model. The core equations of this model consist of a differential balance equation and a current equation, which is derived from space-charge limited conduction. Comparison with experimental data shows that the model successfully reproduces the key features of the measured switching behavior across a wide temperature range, spanning from 80 to 300 K. Additionally, we implement the model in SPICE, enabling circuit-level simulations. The resulting compact model provides a useful framework for guiding experimental studies, capturing key features of the switching behavior, and bridging the gap between device-level characterization and circuit-level design.