This thermodynamic study examines the principles governing energy efficiency and specific energy requirement intrinsic to thermal desalination processes. The practical performances of desalination technologies are investigated and related to the fundamental physical limitations of the processes. The energy efficiency of any thermal desalination process fulfils a limitation similar to the well-known Carnot law for heat engines. The efficiency of a single-effect distiller is limited by a function of the boiling point elevation of the solution. Further analysis shows that, although this can appear as paradoxical, a higher energy efficiency is obtained by a solution with higher boiling point elevation. For multiple-effect distillation, the limit also depends on the temperature drops across the heat exchangers. Comparison with empirical data indicates that these limits are actually approached in real plants. Our study discusses the thermodynamic framework for understanding the performances of thermally-driven desalination technologies, emphasizing the role of the boiling point elevation. The results can be also seen as rules-of-thumb for designing and evaluating the performances of a multiple-effect distillation unit, based only on the properties of the solution to be distilled, in particular, the boiling point elevation.