Heat flow transducers have been implemented within a thermometric fixed-point cell operated with indium. Then a local heat flow rate was monitored simultaneously with the classical temperature measurement. A specific configuration, so-called cell-within-cell, allowed us to control a melting transition plateau and to observe the behaviour of the heat exchanged during the whole process of the melting transition. Owing to their dynamic character, heat flow measurements prove to be the most appropriate for defining specific boundaries on a given transition plateau, and relevant sensors are found to be suitable tools to be coupled with enhanced temperature measurements. This piece of work is presented in two parts, with the description of the set-up and measurement results in this first paper and their subsequent thermodynamic implications in the following one.