Applying small-angle neutron scattering (SANS) on isotopically labeled samples, we have characterized the thermally driven concentration fluctuations (TCFs), one of the main factors in the phenomenology of blend dynamics, in mixtures of styrene-butadiene rubber (SBR) and oligomers of polystyrene (PS) with different compositions. This system displays a large dynamic asymmetry and is thus a good model to explore the tunability of properties of interest in the rubber industry. The SANS experiments, complemented with neutron diffraction with polarization analysis, have allowed one to determine the UCST behavior of the blend and establish its phase diagram. We find a close T-T PS geff vicinity of the spinodal and vitrification lines for 0 intermediate concentrations and samples rich in PS. This induces the freezing of the correlation length for TCF when decreasing the temperature and also has an impact on the reported dielectric response of these mixtures. Furthermore, we have deduced the relevant length scale for segmental relaxation from the comparison of SANS and dielectric results. The values found (approximate to 1.5-2 nm) are close to the Kuhn lengths of the components. The relevance of nanometric length scales in this system could also be tentatively attributed to an underlying nanodomain structure associated with the segregation of phenyl rings and main chains, supported by complementary X-ray diffraction experiments.