We have investigated the thermal behavior of a set of model linear thermoplastic polyurethanes (TPU) with a relatively high content of hard segments: from 50 to 100 wt %. The soft segment of these samples consists of poly(propylene oxide), end-capped with ethylene oxide (EO-PPO-EO), while the hard segment is composed of a 4,4'-methylenediphenylene isocyanate (4,4'-MDI) chain extended by a short diol chain, 2-methyl-1,3-propanediol (MP-Diol). In the present article, we have investigated the origin of the endotherms observed when samples are annealed below the glass transition of the hard segments T-gHS. The work was carried out using mainly differential scanning calorimetry (DSC) and small-angle and wide-angle X-ray scattering (SAXS and WAXS). The so-called "annealing endotherm", T-A, was observed 20-30 degrees C above the annealing temperature. The temperature and enthalpy of T-A were found to increase linearly with the logarithm of the annealing time. This endotherm was assigned to the relaxation (physical aging) of the interfacial materials. With increasing annealing temperature a change in the appearance of the hard phase glass transition, T-gHP, was observed. For long annealing times T-gHP is observed as an endotherm on the DSC thermographs. It is suggested that some of the hard segments undergo relaxation below T-gHs resulting in an enthalpy relaxation endotherm being present below or around T-gHP. An additional endotherm, T-M', was observed as a shoulder at high temperature, just below the microphase mixing transition, T-MMT. This endotherm is thought to be due to the ordering during the phase separation process of the hard segment present in the mixed phase. Finally T-MMT was observed at all annealing temperature used suggesting that even at low annealing temperatures phase separation occurs. The delay time before phase separation starts and the maximum absolute degree of phase separation reached are found to increase with increasing annealing temperature. Our results suggest that a "thermodynamic equilibrium" is reached for each annealing temperature at long enough annealing times.