The rapid thinning of the ice shelves in the Amundsen Sea is generally attributed to basal melt driven by warm water originating from the continental slope. We examine the hypothesis that processes taking place on the continental shelf contribute significantly to the interannual variability of the ocean heat content and ice shelf melt rates. A numerical model is used to simulate the circulation of ocean heat and the melt of the ice shelves over the period 2006–2013. The fine model grid (grid spacing 1.5 km) explicitly resolves the coastal polynyas and mesoscale processes. The ocean heat content of the eastern continental shelf exhibits recurrent decreases around September with a magnitude that varies from year to year. The heat loss is primarily caused by surface heat fluxes along the eastern shore in areas of low ice concentration (polynyas). The cold winter water intrudes underneath the ice shelves and reduces the basal melt rates. Ocean temperatures upstream (i.e., at the shelf break) are largely constant over the year and cannot account for the cold events. The cooling is particularly marked in 2012 and its effect on the ocean heat content remains visible over the following years. The study suggests that ocean‐atmosphere interactions in coastal polynyas contribute to the interannual variability of the melt of Pine Island Glacier. Key Points: Model study with an eddy‐resolving ice‐ocean model covering entire Amundsen Sea Winter cooling within polynyas is responsible for cold anomalies in September Coastal processes contribute to interannual variability of melt of glaciers