A diurnal 'thermal pumping' mechanism is proposed to explain why undersaturation of inert gases may develop at the sea surface during extended periods of low wind speed and net warming. A simple two-layer model of the upper ocean with parameterized air-sea gas exchange is used to explain the process. The model predicts maximum undersaturations of 0.25% for Ne, 0.75% for N2, 0.88% for Ar, and 1.12% for Kr for an assumed diurnal warming signal of 2¿C, a gas transfer rate appropriate to a wind speed of 4 ms-1, and the simplifying assumption of no net warming over the day. The model results depend on the air-sea gas transfer rate and the details of the upper ocean heating and mixing cycle. Observations of N2 undersaturation from the tropical Atlantic provide supporting experimental evidence.