Dynamic thermal gradient-based processes for directed self-assembly of block copolymer (BCP) thin films such as cold zone annealing (CZA) have demonstrated much potential for rapidly fabricating highly ordered patterns of BCP domains with facile orientation control. As a demonstration, hexagonally packed predominantly vertical cylindrical morphology, technologically relevant for applications such as membranes and lithography, was achieved in 1 pm thick cylinder-forming PS-b-PMMA (cBCP) films by applying sharp thermal gradients (CZA-Sharp) at optimum sample sweep rates. A thorough understanding of the molecular level mechanisms and pathways of the BCP ordering that occur during this CZA-S process is presented, useful to fully exploit the potential of CZA-S for large-scale BCP-based device fabrication. To that end, we developed a customized CZA-S assembly to probe the dynamic structure evolution and ordering of the PS-b-PMMA cBCP film in situ as it undergoes the CZA-S process using the grazing incidence small-angle X-ray scattering (GISAXS) technique. Four distinct regimes of BCP ordering were observed within the gradient that include microphase separation from an "as cast" unordered state (Regime I), evolution of vertical cylinders under a thermally imposed strain gradient (Regime II), reorientation of a fraction of cylinders due to preferential substrate interactions (Regime III), and finally grain-coarsening on the cooling edge (Regime IV). The ordering, pathway in the different regimes is further described within the framework of an energy landscape. A novel aspect of this study is the identification of a grain-coarsening regime on the cooling edge of the gradient, previously obscure in zone annealing studies of BCPs. Such insights into the development of highly ordered BCP nanostructures under template-free thermal gradient fields can potentially have important ramifications in the field of BCP-directed self-assembly and self-assembling polymer systems more broadly.