The heating process of a series of new crystalline-amorphous diblock copolymers, hydrogenated polynorbornene-block-hydrogenated poly(1,4-methano-1,4,4a,9a-tetrahydrofluorene) (hPNB-b-hPMTF), has been investigated using time-resolved small-angle X-ray scattering with synchrotron radiation. When the crystalline hPNB block was the major component in hPNB-b-hPMTF, the crystallization temperature of hPNB blocks at the maximum rate Tc* (i.e., the peak temperature of DSC exotherms during cooling at −5 °C/min) was found to be nearly the same to the glass transition temperature Tg of amorphous hPMTF blocks. For these copolymers, the excess upturn scattering at low angles was transiently observed during the melting of hPNB blocks, which depended significantly on the composition and the thermal history applied to hPNB-b-hPMTF before heating. The crystallized lamellar morphology (i.e., an alternating structure consisting of hPNB lamellar crystals and amorphous hPNB + hPMTF layers), which had been gradually transformed from the molten microdomain structure by the crystallization of hPNB blocks, was responsible for the emergence of this scattering, because the excess X-ray intensity was proportional to the volume fraction of the crystallized lamellar morphology existing in the system. We discussed the possible origin of this excess scattering by considering the morphological change during melting.