We present and discuss an improved approach to modeling some aspects of the melting transitions in alkanes, based on the use of single-chain shape descriptors. These descriptors characterize the interplay between molecular shape and chain flexibility as a function of the temperature. In particular, we provide a detailed analysis of the mean (dynamic) molecular shape of single alkane chains at the melting point temperature. By using the known melting points, our aim is to test whether one can estimate the length of the alkane chain exhibiting the first premelting transition. To this end, we have determined the number of carbon atoms required to produce liquidlike conformations whose average shape at the melting point is the same as that of a typical conformer in premelting phase. Our results agree closely with experiments, indicating that the first premelting transition takes place in nonane (n = 9). We believe that the present approach may provide an avenue to extend the use of single-chain shape descriptors for modeling other phenomena that depend on chain flexibility.