Humans rely on auditory information to estimate the path of moving sound sources. But unlike in vision, the existence of motion-sensitive mechanisms in audition is still open to debate. Psychophysical studies indicate that auditory motion perception emerges from successive localization, but existing models fail to predict experimental results. However, these models do not account for any temporal integration. We propose a new model tracking motion using successive localization snapshots but integrated over time. This model is derived from psychophysical experiments on the upper limit for circular auditory motion perception (UL), defined as the speed above which humans no longer identify the direction of sounds spinning around them. Our model predicts ULs measured with different stimuli using solely static localization cues. The temporal integration blurs these localization cues rendering them unreliable at high speeds, which results in the UL. Our findings indicate that auditory motion perception does not require motion-sensitive mechanisms.