The process of melting in polycrystalline systems based on a single crystalline phase is studied. The thermodynamic inhomogeneity of such systems is demonstrated. In polycrystalline systems the onset of melting takes place at temperatures substantially lower than the melting point; it can be treated as a sequence of transformations, namely the melting of grain-boundary and surface (non-autonomous) phases, and the transition of the crystalline (solid-state autonomous) phase into a non-autonomous liquid phase. A mathematical model is constructed describing the temporal distribution of the thermal effect of melting as a function of the thermodynamic and kinetic properties characterizing autonomous and non-autonomous phases of the system, the mean grain size, and the sample heating rate. An effect, known as pre-melting in the literature, is described quantitatively. Modes of thermal analysis are described that, by allowing for the grain size, ensure the most accurate determination possible of the melting temperatures of the autonomous and non-autonomous phases.