We have investigated the ordering processes from the disordered-sphere phase (designated hereafter disordered sphere), where spherical microdomains exist but they have only a short-range liquidlike order, to the phase of hexagonally packed cylindrical microdomains (designated hereafter hex-cylinder), induced by the temperature drop (T-drop). The block copolymer studied is a compositionally asymmetric polystyrene-block-polyisoprene-block-polystyrene triblock copolymer and forms disordered sphere above the order-disorder transition temperature involving the lattice disordering-ordering transition temperature, T-ODT or T-LDOT, spheres in a body-centered-cubic lattice (designated hereafter bcc-sphere) below T-LDOT but above the order-order transition (OOT) temperature, T-OOT, and hex-cylinder below T-OOT. The ordering processes induced by T-drop were explored in situ and at a real time by using time-resolved small-angle X-ray scattering, and the transient microdomain structures developed during the ordering processes were observed by a transmission electron microscope and a polarized optical microscope for specimens rapidly frozen below the glass transition temperature at particular times in the ordering processes. We confirmed that the freeze-in process does not change the long-range order of the system. When the specimen is deeply quenched into the temperature range below T-OOT, hex-cylinder is directly formed from disordered sphere. However, when the specimen is shallowly quenched below T-OOT, bcc-sphere is first formed from disordered sphere and fills the whole sample space. Then bcc-sphere is transformed into hex-cylinder. This striking ordering process first involves the ordering into a metastable structure followed by the OOT into a stable structure.