Time-resolved small-angle neutron scattering (SANS) experiments have been performed on the self-assembling process of a binary mixture of deuterated polybutadiene and protonated polybutadiene at the critical composition. This mixture has an upper critical solution temperature type of phase diagram with the spinodal temperature at 99.2-degrees-C. Specimens held in the single-phase state at an initial temperature (T(i)) were quenched to a point inside the spinodal phase boundary at a final temperature (T(f)) to induce phase separation via spinodal decomposition (SD). In order to examine the effect that thermal concentration fluctuations have on SD, three different initial temperatures, T(i) = 102.3-degrees-C, 123.9-degrees-C, and 171.6-degrees-C, were chosen while T(f) was fixed at -7.5-degrees-C. The time-dependent SANS structure factor, S(q,t;T(f)), showed clear scattering peaks corresponding to the early and intermediate stages of SD. The time changes in the wave number q(m)(t;T(f)) and the intensity S(m)(t;T(f)) at the peak of S(q,t;T(f)) followed different paths depending on the initial temperature. This fact evidences a definite effect of thermal concentration fluctuations on SD (i.e., a significant ''memory'' effect). A critical test of the linearized Cahn-Hilliard-Cook theory led to the conclusion that this theory can describe satisfactorily the early stage SD in the deep-quench region.