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We had introduced a microscopic technique to obtain heat capacity peaks near first-order phase transitions in polycrystalline phase change materials (PCMs). Such PCMs are composed of a large number of segments or grains, so that the total heat capacity of a PCM is a double average of heat capacities in the individual grains. One average is over surface (or boundary) effects occurring due to interactions of grains with their surroundings, while the other average is over grain sizes. Using this approach, we were able to derive a formula for heat capacity peaks and use it to very accurately fit experimental data for three selected PCMs measured by adiabatic scanning calorimetry. The fitted values of the phase change temperature for these three PCMs were not convincing, however. In this paper we argue that the reason for this controversy stems from too a crude approximation of surface effects that was used originally. Therefore, here we propose an improvement of our technique by suggesting a more appropriate approximation that still leads to as accurate fits as the original one. We illustrate this for one of the three PCMs. [ABSTRACT FROM AUTHOR]