Analysis of the dependence of the melting temperature on the crystallization temperature has been frequently used to estimate the equilibrium melting temperature of a polymer. In the present paper the underlying basis for this extrapolative method is examined in detail. Two distantly different types of nucleation are considered. One is the Gibbs two-dimensional nucleus; the other, certain kinds of three-dimensional nuclei. Thickening, subsequent to nucleation, is also taken into account. Appropriate experiments with linear polyethylenes that have most probable molecular weight distributions, as well as with a molecular weight fraction, were carried out over a wide range in crystallization temperatures. Three distinct regions are observed. The high-temperature region is curved and precludes an extrapolation of the data to the equilibrium melting temperature. Reasons for this behavior are presented. Evidence for its being a general phenomenon is also given. A melting temperature of 141 degrees C was directly observed for linear polyethylene.