This second part of the work is devoted to the thermodynamic implications of the results presented in the preceding paper, as heat flow meters (HFMs) were installed within a thermometric fixed-point cell operated with indium. Then, simultaneous measurements of both temperature and heat flow allow us to pinpoint the specific boundaries (solidus and melt-off points) of a given transition plateau. To the best of our knowledge, this work is the first experimental illustration being reported on how to consider a plateau as a specific thermodynamic regime marked with a minimum amount of generated entropy in a metrological fixed-point cell. As a result, a significant relationship linking the boundaries of the plateau and the melting temperature of the material studied is presented. In order to obtain a quantitative understanding of the quality of a given transition process, straightforward thermodynamic considerations allow us to consider both theoretically and experimentally an adimensional parameter defined as the ratio of the entropy generation over the entropy change.