An asymmetric poly(ethylene-propylene)-poly(ethylethylene) (PEP-PEE) di-block copolymer was examined near the order-to-disorder transition temperature, TODT, by small-angle neutron scattering as a function of shear rate, γ̇. Heating in the absence of shear disorders the material from a hexagonal structure at TODT = 155 ± 1°C. Application of a reciprocating simple shear field markedly influences the phase behaviour near the ODT. Application of shear while heating increases TODT consistent with the theoretical prediction, TODT ∼ γ̇2. During fast cooling studies we observe an additional characteristic temperature, TS, at which the material spontaneously orders, which we interpret as a stability (i.e., spinodal) limit. This result also agrees with the theoretical prediction, τS ∼ γ̇-1/3. Upon cessation of shear at temperatures close to but above the quiescent TODT a transient phase is observed before the system macroscopically disorders. The transient structure has a symmetry compatible with spheres arranged on a body centered cubic (BCC) space lattice, or undulating cylinders of the minority component (PEE). Anisotropic (i.e. lattice pinned) fluctuations can also be observed close to, but below, TODT upon heating the hexagonal structure under shear free conditions.