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Central and autonomic nervous system activities are coupled during sleep. Cortical slow oscillations (SOs; <1 Hz) coincide with brief bursts in heart rate (HR), but the functional consequence of this coupling in cognition remains elusive. We measured SO–HR temporal coupling (i.e., the peak-to-peak interval between downstate of SO event and HR burst) during a daytime nap and asked whether this SO–HR timing measure was associated with temporal processing speed and learning on a texture discrimination task by testing participants before and after a nap. The coherence of SO–HR events during sleep strongly correlated with an individual's temporal processing speed in the morning and evening test sessions, but not with their change in performance after the nap (i.e., consolidation). We confirmed this result in two additional experimental visits and also discovered that this association was visit-specific, indicating a state (not trait) marker. Thus, we introduce a novel physiological index that may be a useful marker of state-dependent processing speed of an individual.