The double-crossing hypothesis posits that post-perovskite bearing rock in Earth's D″ layer exists as a layer above the core-mantle boundary bounded above and below by intersections between a curved thermal boundary layer geotherm and a relatively steep phase boundary. Increasing seismic evidence for the existence of pairs of discontinuities predicted to occur at the top and bottom of this layer motivates an examination of the consistency of this model with mineral physics constraints for the Clapeyron slope of this phase transition. Using independent constraints for a lower bound on temperature in Earth's deep mantle and the temperature of Earth's inner core boundary, we show that a post-perovskite double-crossing is inconsistent with plausible core temperatures for a Clapeyron slope less than about 7 MPa/K, with the higher range of experimental values yielding better agreement with recent estimates of the melting temperature of Earth's core.