In a previous paper (Macromolecules 2007, 40, 5923), we reported that a zone heating method, which imposes the moving temperature-gradient (del T) field on ordering process of various melts in general, enabled to control a macroscopic orientation of hexagonally packed cylindrical microdomain structures (hex-cyl) of block copolymer (bcp) bulk. In this report, we have investigated how the variation of the moving rate of del T affects the macroscopic orientation by using two kinds of polystyrene-block-polyisoprene bcps having different mobility. We found that the upper limit of the moving rate required to induce the unique texture and orientation of hex-cyl became large with increasing the mobility of the bcps. These results indicate that the moving rate should be smaller than the intrinsic growth rate of the hex-cyl grains in the undercooled disordered melt.