A model of the RESET melting process in conventional phase-change memory (PCM) devices is constructed in which the Gibbs–Thomson (GT) effect, representing local equilibrium at the solid–liquid interface, is included as an interfacial condition for the electro-thermal model of the PCM device. A comparison is made between the GT model and a commonly used model in which the interfacial temperature is fixed at the bulk melting temperature of the PCM material. The model is applied to conventional PCM designs in which a dome-shaped liquid/amorphous region is formed. Two families of solutions are computed representing steady state liquid regions, distinguished by their thermodynamic aspects. There is a family of solutions representing a hypothetical liquid nucleation process, and a family of larger steady-state liquid solutions representing the limit of the melting process. These ‘melting limits’ enable calculation of minima in voltage and corresponding current required for the RESET process. In this PCM configuration, the GT effect constrains the equilibrium solid–liquid interface temperature to remain above the bulk melting temperature during melting. The magnitude of this temperature difference increases with decreasing device size scale, thus requiring an increase in the required voltage and current needed for RESET compared to the case in which the interface temperature is approximated by the bulk melting temperature. This increase becomes substantial for active device dimensions in the <20 nm range. The impact of this phenomena on PCM device design is discussed.