We present results from new geophysical data allowing modelling of the water flow within Subglacial Lake Ellsworth (SLE), West Antarctica. Our simulations indicate that this lake has a novel temperature distribution due to significantly thinner ice than other surveyed subglacial lakes. The critical pressure boundary (tipping depth), established from the semi-empirical Equation of State, defines whether the lake's flow regime is convective or stratified. It passes through SLE and separates different temperature (and flow) regimes on either side of the lake. Our results have implications for the location of proposed access holes into SLE, the choice of which will depend on scientific or operational priorities. If an understanding of subglacial lake water properties and dynamics is the priority, holes are required in a basal freezing area at the North end of the lake. This would be the preferred priority suggested by this paper, requiring temperature and salinity profiles in the water column. A location near the Southern end, where bottom currents are lowest, is optimum for detecting the record of life in the bed sediments; to minimise operational risk and maximise the time span of a bed sediment core, a location close to the middle of the lake, where the basal interface is melting and the lake bed is at its deepest, remains the best choice. Considering potential lake-water salinity and ice-density variations, we estimate the critical tipping depth, separating different temperature regimes within subglacial lakes, to be in about 2900 to 3045 m depth.