Lyotropic lamellar phases under shear flow have been shown to form multilamellar vesicles (MLVs), an onion-like structure. The size of the vesicles is governed by the shear imposed on the sample. Previously, we studied the structural transformation from multilamellar vesicles to lamellae to sponge under shear. Here, we focused only in the MLV region, L-alpha(*), of a temperature sensitive surfactant system (C12E4-water) to investigate the packing of multilamellar vesicles as a function of temperature under constant shear. Two sets of temperature scan experiments were performed in the L-alpha(*) phase using the noninvasive small-angle neutron scattering (SANS) technique, one while heating and the other while cooling the sample. Data from the heating and cooling cycles were used to demonstrate reversibility of the system. Three states of packing can be identified from the scattering profiles: isotropic at low (i) and high (iii) temperature ranges, and hexagonal with six spots at an intermediate temperature interval (ii). The hexagonal 2-D SANS patterns reveal different peak intensities under shear, which upon cessation of shear relaxes to a symmetrical scattering pattern. The hexagonal scattering pattern from state ii is a layering effect of vesicles into a honeycomb type structure (spherulites).