Thickness measurements of Southern Ocean sea ice are very sparse and satellite altimetry still provides relatively uncertain estimates of ice thickness. The only tool for monitoring sea ice thickness over long periods of time with sufficient accuracy are moored upward looking sonars (ULS). The instruments measure the subsurface portion (draft) of the ice by recording the travel times of sonar signals (Fig. 1). We present ULS data from the central Weddell Sea, where the sea ice starts forming in April and disappears in January of the following year (length of growth period: ~180 days). We use the data together with Stefan's Law to estimate the two quantities that limit the maximum thermodynamic ice growth in austral winter to about 1 m: (a) The snow cover on top of the ice and (b) the oceanic heat flux from below.