Traditional electronic devices are well-known to improve in speed and energy-efficiency as their dimensions are reduced to the nanoscale. However, this scaling behavior remains unclear for nonlinear dynamical circuit elements, such as Mott neuron-like spiking oscillators, which are of interest for bio-inspired computing. Here we show that shrinking micrometer-sized VO2 oscillators to sub-100 nm effective sizes, achieved using a nanogap cut in a metallic carbon nanotube (CNT) electrode, does not guarantee faster spiking. However, an additional heat source such as Joule heating from the CNT, in combination with small size and heat capacity (defined by the narrow volume of VO2 whose insulator-metal transition is triggered by the CNT), can increase the spiking frequency by ~1000x due to an electro-thermal bifurcation in the nonlinear dynamics. These results demonstrate that nonlinear dynamical switches operate in a complex phase space which can be controlled by careful electro-thermal design, offering new tuning parameters for designing future biomimetic electronics.