To utilize the full potential of block copolymer (BCP) thin films for use in technological devices ranging from ion conduction membranes and transistors to nanowire array antennas, rapid self-assembly of lamellar block copolymers (l-BCPs) with vertically oriented lamellar domains on a variety of unmodified substrates is needed. l-BCPs have an inherently larger interfacial area for transport compared to their cylindrical counterpart. Our observations demonstrate that the as-cast weakly ordered vertically oriented state of l-BCP films of polystyrene-block-poly(methyl methacrylate) (PS-b-PMMA) from the directional evaporation of select solvents act as "seed templates" for their ultra-fast evolution (approximate to 130 s) into well-ordered vertically oriented nanostructures, using a thermal gradient-based cold zone annealing (CZA) technique. Vertical lamellae are obtained on unmodified substrates, Quartz and Kapton, and the kinetics of l-BCP ordering is much faster by CZA as compared to the isotropic oven annealing. The rapid ordering kinetics of vertical l-BCPs is tested and found applicable to different molecular masses and film thicknesses ranging from 20 nm to 480 nm, which ultimately flip over to their equilibrium parallel morphology at the upper limits of annealing times. This rapid ordering strategy for the vertical orientation of l-BCPs using roll-to-roll compatible CZA would be highly relevant for fundamental studies of interfacial transport as well as for industrial applications from membranes to nanowires.