A widely used method for investigating palaeotemperatures is to analyze local proxy records (e.g. ice cores or deep-sea sediment cores). The interpretation of these records is often not straightforward, and global or hemispheric means cannot be deduced from local estimates because of large spatial variability. Using a different approach, temperature changes over the last glacial cycle can be estimated from sea-level observations by applying an inverse method to an ice-sheet model. In order to understand the underlying physical mechanisms, we used a 1-D ice-sheet model and a 3-D coupled thermodynamic ice-sheet–ice-shelf–bedrock model to investigate the importance of several physical processes for the inverse temperature reconstructions. Results show that (i) temperature reconstructions are sensitive to the employed formulation of mass balance, (ii) excluding thermodynamics in the ice sheet leads to a smaller temperature amplitude in the reconstruction and (iii) hysteresis in the non-linear relation between sea level and temperature occurs as a consequence of ice redistribution in the process of merging and separation of ice sheets. The ice redistribution does not occur if the geometry does not support the formation of a relatively flat dome, which tends to be preserved in warming conditions.