In this work, we investigate the intrinsic cycle-to-cycle variations in a spiking temperature-sensitive neuron, based on the resistive switching of a Vanadium dioxide (VO2) two-terminal device. We study how this phenomenon impacts the spike rate jitter, and affects the spiking sensor precision. To do so, we combine a statistical analysis of the device DC characteristics, with measurements of the spiking neuron in dynamic operation from 41 to 47 degrees C. Using an analytical dynamic model, we reveal that the VO2 cycle-to-cycle variations of the insulating resistance and insulator-to-metal threshold voltage dominate the stochastic processes. Our spiking sensor achieves large, linear sensitivity (1.71 kHz/degrees C) and high resolution (0.024 degrees C for a 10 ms-long observation), attributed to its small cycle-to-cycle variations.