Laboratory experiments with overturning circulation driven by oscillatory heat fluxes at one boundary are used to explore implications, for the ocean stratification, of a cyclic fluctuation in sea-surface buoyancy forcing. Fluctuations having a range of periods spanning the timescale for global recycling of the ocean volume through the thermocline are considered, with emphasis on inter-hemispheric 'see-saw' oscillations. Episodic sinking of dense water in the oceans is represented by convection in a channel with a base that is cooled over a central region and subjected to oscillatory heating near both ends, while providing a constant total heat input. For this simplified system the time-average interior temperature is found to be insensitive to the forcing period, but does vary with oscillation amplitude, whereas the interior fluctuations increase with forcing period. The circulation and density field are significantly different from those given by a steady forcing equal to the time-average of the actual oscillatory forcing, even for high-frequency oscillations. The results indicate that the overall stratification lies between that expected from the strongest phase of deep sinking and that given by symmetric sinking in both hemispheres. Glacial cycles are predicted to involve significant temperature fluctuations in the abyssal ocean. However, they are too short for the ocean to remain in quasi-equilibrium with the changing boundary conditions.