Thermal coupling links between multicomponent distillation columns are known to reduce the total heat duty and, therefore, the first-law energy demand of distillation configurations. Most studies on the energy savings of thermally coupled configurations have focused on cases where all thermal coupling links of a configuration have been used. We show that certain types of thermal coupling links of a configuration actually do not contribute to the first-law energy savings. Furthermore, it is often believed that the first-law energy savings due to thermal coupling links always has associated second-law temperature-level costs due to increased utility demand at extreme temperatures. However, we demonstrate that some types of thermal coupling links provide first-law energy savings without exhibiting any second-law temperature-level penalties. Finally, we present heuristics to enable quick identification of such thermal coupling links.