A small-angle neutron scattering study of the temperature dependence of the micellar structure has been performed on a 1% w/w aqueous solution of the poly(oxyethylene)-poly(oxypropylene)poly(oxyethylene) (POE-POP-POE) block copolymer Synperonic P-85 using a Poiseuille-geometry shear now apparatus. The system is characterized by two transition temperatures. The first is the critical micellization temperature at 24 degrees C. This marks the lower boundary of a spherical, later more ellipsoidal, micellar phase. The next transition is at 62 degrees C, above which the micelles may be adequately modeled as rigid rods. By 73 degrees C, rods with diameters of 10-12 nm and lengths of almost 400 nm have been attained. This micellar growth takes place without any appreciable increase in the radius of the micelles. The response of the rodlike micelles to the presence of the shear flow field is also reported.