Ice sheets such as Pine Island and Thwaites Glaciers which terminate at their ice shelves in the eastern Amundsen Sea, West Antarctica, are losing mass faster than most others about the continent. The mass loss is due to basal melting, this affected by a deep current thought to be guided by bottom bathymetry that transports warm Circumpolar Deep Water (CDW) from the continental shelf break towards the ice shelves. This current and associated heat transport are controlled by the near-surface winds that vary on a range of timescales due to both anthropogenic and natural effects. In this study we use idealised models to reproduce essential features of the Amundsen Sea circulation and heat transport. The aim is to elucidate the role of bathymetric features in shaping the circulation and in enabling heat transport from the deep ocean onto the continental shelf. Bathymetric variations along the continental slope enhance on-shelf heat transport by inducing breaks in the Antarctic Slope Front that separates off-shelf CDW from the colder, fresher shelf waters. The idealised model results imply that a ridge that blocks deep westward inflow from the Bellingshausen Sea leads to the existence of a deep cyclonic circulation on the shelf. Part of this circulation is an eastward undercurrent that flows along the continental shelf break. The broader cyclonic circulation transports heat that has been recently fluxed onto the shelf towards the south. These fundamental investigations will help refine the aims of future fieldwork and modelling.