The reality of modern power grids requires the use of flexibilities from generation, load and storage. These flexibilities allow system operators to modify a transformer loading in a smart way. Therefore, power constraints of transformers can be overcome by using the appropriate flexibility. However, transformers have a physical limit of energy transfer which cannot be overpassed. This energy limit represents the unique transformer's loading profile, ensuring the highest energy transfer under a given ambient temperature profile. The paper explains how the energy limit can be calculated. Typical characteristics of an energy limit are estimated in cold continental climate of Russia and warm temperate climate in France. Maximal, minimal and mean loadings are identified for each month. Loading durations of energy limit are determined for each cooling system. It is found that winding temperatures of transformers, operating at energy limits, remain in the vicinity of design winding temperature. Therefore, transformer operation at energy limit avoids a high temperature stress and simultaneously maximizes the energy transfer. The application of energy limits for power system problems is briefly explained along the paper. Energy limit application can reduce an energy cost, maximize a renewable generation and increase a hosting capacity of distribution network. This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.