The melting and crystallization of indium has been reinvestigated with the heater-controlled Mettler–Toledo differential scanning calorimeter DSC 820. The heat-flow rate during melting and crystallization is largely determined by instrumental characteristics and often does not permit the evaluation of kinetic parameters of the phase transition. We found that the observed reversing character of the melting depends strongly on the modulation parameters. For quasi-isothermal, temperature-modulated calorimetry with a symmetric sawtooth, the degree of reversibility decreases with increasing amplitude of temperature modulation. At a lower average temperature of modulation relative to the melting temperature, the partial melting process can be fully reversing, while at higher average temperatures, the melting becomes less reversing due to instrumental time restrictions for the completion of melting. With an appropriately modified, nonsymmetric sawtooth, however, the phase transition can be made fully reversing, even in the later stages of the melting process (as long as crystal nuclei remain). The influence of sample mass, sample position within the pan, and type of pan are analyzed, and the conditions for the study of the kinetics of crystallization of nucleated crystals close to the melting temperature, and by implication, also the melting kinetics, are suggested.