Negative differential resistance behavior in oxide memristors, especially those using NbO₂, is gaining renewed interest because of its potential utility in neuromorphic computing. However, there has been a decade-long controversy over whether the negative differential resistance is caused by a relatively low-temperature non-linear transport mechanism or a high-temperature Mott transition. Resolving this issue will enable consistent and robust predictive modeling of this phenomenon for different applications. Here we examine NbO₂ memristors that exhibit both a current-controlled and a temperature-controlled negative differential resistance. Through thermal and chemical spectromicroscopy and numerical simulations, we confirm that the former is caused by a ~400 K non-linear-transport-driven instability and the latter is caused by the ~1000 K Mott metal-insulator transition, for which the thermal conductance counter-intuitively decreases in the metallic state relative to the insulating state.The development of future computation devices will be aided by a better understanding of the physics underlying material behaviors. Using thermoreflectance and spatially resolved X-ray microscopy, Kumar et al. elucidate the origin of two types of negative differential resistance in NbO₂ memristors.