The Weddell Polynya, a large expanse of water that originated over Maud Rise (a bathymetric protrusion centred near 64°30′S, 3°E) and remained open during winter in the late 1970s, may have manifested a mode of deep ocean convection where despite large heat loss at the surface, sustained heat transport from below prevents lasting ice formation. In a different dominant mode (the present one), sea ice forms early in the winter and subsequently provides a thermal barrier that quickly quells incipient deep convection, thus preventing wholesale destruction of the ice cover. A possible mechanism for overcoming the thermal barrier is thermobaricity, the pressure dependence of the thermal expansion factor for seawater. An idealized, two-layer version of actual temperature and salinity profiles from the Weddell illustrates that thermobaric mixing can persist for extended periods in an ice-covered ocean, provided realistic melt rates (controlled by salt exchange at the ice/ocean interface) are specified. This furnishes a possible explanation for transient winter polynyas sometime observed in the ice-covered Southern Ocean. Thermobaricity may provide a trigger for widespread convection with possible climate impact.