The first high-temperature endotherm (T-1) of polyurethane hard segment based on 4,4＇-diphenylmethane diisocyanate (MDI) and 1,4-butanediol (BD) was studied by differential scanning calorimetry (DSC). The materials contain 69% (w/w) of MDI and BD as the hard segment and hydroxyl-terminated cis-polybutadiene with number average molecular weights of 1650 and 2300, respectively, as the soft segment. The hard segment and the soft segment of these polyurethanes appear to be very completely phase-separated, giving rise to very simplified material structures for this study. Samples under melt-quenched condition gave rise to a highly amorphous phase for the hard phase and a distinct hard-segment glass transition behavior, which enabled us to study the T-1 behavior in relation to the amorphous hard-segment T-g (T-gh). Upon annealing below the T-gh of the pure amorphous hard phases, both the T-1 temperature and magnitude of the T-1 endotherm increased linearly with the increase in logarithmic annealing time (log t(a)). On the other hand, if the polyurethane were first annealed to form multiple endotherms at noncrystalline T-2 region, the annealing above the previous T-gh gave rise to a T-1 which also increased linearly in temperature with the increase in log t(a). These phenomena are typical of enthalpy relaxations resulting from the physical aging of the amorphous hard segment. Thus, we suggest the long-term confusing nature of T-1 is due to an enthalpy relaxation of the amorphous hard segment. On the other hand, we also suggest that T-2, which was previously associated with a long-range order of unspecified nature, would disturb the amorphous hard segment and cause a rise in the T-g in different degrees to a higher temperature near T-2.