Thin sea ice plays a central role in the surface heat and mass balance of the Arctic Ocean. In order to develop understanding of these balances we describe and analyze highly resolved temperature data taken through the air/sea/ice interface during the transition from an ice‐free to an ice‐covered Arctic Ocean surface. The data were taken to observe the thermodynamic evolution of a lead, a process that has previously only been accessible to measurement techniques confined to the lead edge. Our detailed analysis of the field data is guided by recent theoretical and experimental advances in understanding the phase dynamics of directionally solidified alloys. Because of the dearth of direct observations we also present time series of the relevant heat fluxes inferred from our data and demonstrate the controlling influence that the internal phase evolution has on these quantities. We have previously examined the stability of the brine trapped in a growing sea ice matrix both theoretically and experimentally and now find that haline convection, driven from within the growing layer, is consistent with this previous work and with the nature of direct turbulence measurements. The importance of this process is that although ice growth is continuous, the local brine flux commences abruptly, only after some time, in contrast to what had previously been supposed. Hence the ice growth process itself is a source of intermittency in oceanic boundary layer turbulence. Furthermore, we find that in this particular situation the sea ice growth is not simply a square root function of time, in contrast to the model typically used in numerical simulations. By far the most practical methods of studying lead convection are numerical simulations and laboratory models, and a strong conclusion of this study is the importance of the proper treatment of the boundary conditions describing the buoyancy f