Small-angle x-ray scattering experiments were performed on concentrated dispersions in benzene, of silica particles coated with octadecyl-chains. Such dispersions are known to exhibit short-ranged attractive particle-interactions which depend on the temperature. At sufficiently low temperature, the attraction gives rise to a reversible phase-separation. In the present study, use was made of this phenomenon to fractionate the system. By analyzing two different fractions, the role of polydispersity in the attractive behavior was investigated. For both original and fractionated material, scattering curves were measured using a Kratky-camera equipped with a stepscanning setup and monitor-detector. The concentrations investigated were 0.033, 0.363, 0.496, and 0.628 g/ml, at temperatures ranging from 25-degrees to 52-degrees-C. From the intensity-patterns of the dilute dispersions, the average radius of the silica-core was found to be 7 nm for both fractions. The scattering curves of the concentrated dispersions were compared with Baxter's adhesive-hard-sphere model, taking the particle size polydispersity into account. For both fractions, a semi-quantitative model description was obtained. At all temperatures, the fit-parameters found show a different particle-stickiness for the two fractions, indicating the existence of a distribution for this property. The temperature dependence of the attraction turned out to be much weaker than in previous studies with larger particles.