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Abstract Melt rates of West Antarctic ice shelves in the Amundsen Sea track large decadal variations in the volume of warm water at their outlets. This variability is generally attributed to wind‐driven variations in warm water transport toward ice shelves. Inspired by conceptual representations of the global overturning circulation, we introduce a simple model for the evolution of the thermocline, which caps the warm water layer at the ice‐shelf front. This model demonstrates that interannual variations in coastal polynya buoyancy forcing can generate large decadal‐scale thermocline depth variations, even when the supply of warm water from the shelf‐break is fixed. The modeled variability involves transitions between bistable high and low melt regimes, enabled by feedbacks between basal melt rates and ice front stratification strength. Our simple model captures observed variations in near‐coast thermocline depth and stratification strength, and poses an alternative mechanism for warm water volume changes to wind‐driven theories.