Experiments on heat transfers inside an emulsion when the dispersed phase crystallizes or melts have previously been presented [Dumas et al., Eurotherm Seminar 5 (1988)]. The crystallization and melting processes are not symmetrical because of the large undercooling induced by the smallness of the emulsion droplet sizes. The space-time evolution of the temperature inside a metallic cylinder filled with the emulsion is investigated. The dispersed substances are either hexadecane, octadecane or water. In Part 1 of this paper we describe the results obtained during a steady cooling. We observe that, largely below the melting temperature, a stabilization of the temperature occurs in the axis region during a lapse of time depending on the cooling rate, the mass fraction or the final temperature. A simplified model based on a combination of the energy equation and the nucleation theories is proposed and explains the main experimental features.