Palaeoclimate records have revealed the presence of millennial-scale climate oscillations throughout the last glacial period1. Six periods of extreme cooling in the Northern Hemisphereknown as Heinrich eventswere marked by an enhanced discharge of icebergs into the North Atlantic Ocean 2,3, increasing the deposition of ice-rafted debris2. Increased sliding at the base of ice sheets as a result of basal warming has been proposed to explain the iceberg pulses4,6, but recent observations7,8 suggest that iceberg discharge is related to a strong coupling between ice sheets, ice shelves and ocean conditions. Here we use a conceptual numerical model to simulate the effect of ocean temperature on ice-shelf width, as well as the impact of the resultant changes in ice-shelf geometry on ice-stream velocities. Our results demonstrate that ocean temperature oscillations affect the basal melting of the ice shelf and will generate periodic pulses of iceberg discharge in an ice sheet with a fringing shelf. We also find that the irregular occurrence of Heinrich events seen in the palaeoclimate records can be simulated by periodic ocean forcing combined with varying accumulation rates of the ice sheet. Our model simulations support a link between millennial-scale ocean temperature variability and Heinrich events during the last glacial period.