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Abstract Marginal ice zones are composed of discrete sea‐ice floes, whose dynamics are not well captured by the continuum representation of sea ice in most climate models. This study makes use of an ocean large eddy simulation (LES) model, coupled to cylindrical sea‐ice floes, to investigate thermal and mechanical interactions between melt‐induced submesoscale features and sea‐ice floes, during summer conditions. We explore the sensitivity of sea‐ice melt rates and upper‐ocean turbulence properties to floe size, ice‐ocean drag, and surface winds. Under low wind conditions, upper ocean turbulence transports warm cyclonic filaments from the open ocean toward the center of the floes and enhances their basal melt. This heat transport is partially suppressed by trapping of ice within cold anticyclonic features. When winds are stronger, melt rates are enhanced by the decoupling of floes from the cold, melt‐induced lens underneath sea ice. Distinct dynamical regimes emerge in which the influence of warm filaments on sea‐ice melt is mitigated by the strength of ice‐ocean coupling and eddy size relative to floe size. Simple scaling laws, which may help parameterize these processes in coarse continuum‐based sea‐ice models, successfully capture floe melt rates under these limiting regimes.