The link between time-of-day and productivity on cognitive tasks is crucial to understand workplace efficiency and welfare. We study the performance of University students taking at most one exam per day in the final two weeks of the semester. Exams are scheduled at different time-of-day in a quasirandom fashion. We find that peak performance occurs around lunchtime (1.30pm), as compared to morning (9am) or late afternoon (4.30pm). This inverse-U shape relationship between time-of-day and performance (i) is not driven by stress or fatigue, (ii) is consistent with the idea that cognitive functioning is an important determinant of productivity and (iii) implies that efficiency gains of up to 0.14 standard deviations can be achieved through simple re-arrangements of the time of exams. While researchers have shown that biological factors influence changes in productivity between day and night shifts, we establish that such relationship is also important within a standard day-light shift. A simple back of the envelope calculation applied to an external context that is likely to benefit from our results, elective surgeries, suggests that a different sorting of the cognitive tasks performed by surgeons may lead to an increase in the number of patients saved.