The phase-separation process and the self-organization of the textures in the biphase region of a thermotropic liquid crystalline polyester sample [poly(4,4’-dioxy-2,2’-dimethylazoxybenzene-dodecanedioyl)] were studied by polarizing light microscopy both during the heating from the fully anisotropic phase to the biphase region and during the cooling from the isotropic phase to the biphase region. The phase separation occurs as a consequence of chain segregation according to the chain length. The phase-separation process is found to be the same for both thermal procedures, but the self-organization of the textures is found to strongly depend on thermal history. The domain structure depends on the thermal history under the heating and cooling cycles employed in this work. The special heating process used in this work developed a fractionation of molecular species in space according to their molecular length which caused a memory effect in the structure evolution during a subsequent cooling process, giving rise to a unique domain structure as described in the text.