A model is presented that describes the simultaneous growth and ablation of a layer of ice between an under-ice melt pond and the underlying ocean. Such false bottoms are the only significant source of ice formation in the Arctic during summer. Analytical solutions for diffusional transport of heat and salt are calculated that illustrate the importance of salt transport in effecting phase change. The model is extended to account for turbulent transports and applied to make predictions of bottom ablation rates of sea ice given the far-field properties of the ocean from the AIDJEX and SHEBA field experiments. The model predictions show that false bottoms may play a significant role in the summer heat budget of the ice-ocean system, causing localized heat fluxes of more than 10 W m-2 into the mixed layer. The thickening of thin ice by false-bottom formation leads to longer-lasting sea ice and thus smaller ice-free areas, which might be an important mechanism affecting the surface albedo.