A general study of the heat transfers inside the cell of a differential scanning calorimeter is presented. In Part 1 of this study, the crystallization of undercooled droplets of an emulsion is analysed. It is demonstrated that the classical assumption of a uniform temperature in the cell cannot explain the shape of the thermogram. The model, which considers the local heating due to the exothermic transformations of the droplets and the erratic character of the crystallizations, shows, despite the small size of the cell, important temperature gradients and explains the shape of the thermogram upon cooling. The analysis indicates that the undercooling is well characterized by the beginning of the peak and not by the peak minimum as suggested before.