Block copolymers (BCPs) are emerging as a cost-effective nanofabrication tool to complement conventional optical lithography because they self-assemble in highly ordered polymeric templates with well-defined sub-20-nm periodic features. In this context, cylinder-forming polystyrene-block-poly(methyl methacrylate) BCPs are revealed as an interesting material of choice because the orientation of the nanostructures with respect to the underlying substrate can be effectively controlled by a poly(styrene-random-methyl methacrylate) random copolymer (RCP) brush layer grafted to the substrate prior to BCP deposition. In this work, we investigate the self-assembly process and lateral order evolution in RCP + BCP systems consisting of cylinder-forming PS-b-PMMA (67 kg mol-1, PS fraction of ∼70%) films with thicknesses of 30, 70, 100, and 130 nm deposited on RCP brush layers having thicknesses ranging from 2 to 20 nm. The self-assembly process is promoted by a rapid thermal processing machine operating at 250 °C for 300 s. The level of lateral order is determined by measuring the correlation length (ξ) in the self-assembled BCP films. Moreover, the amount of solvent (Φ) retained in the RCP + BCP systems is measured as a function of the thicknesses of the RCP and BCP layers, respectively. In the 30-nm-thick BCP films, an increase in Φ as a function of the thickness of the RCP brush layer significantly affects the self-assembly kinetics and the final extent of the lateral order in the BCP films. Conversely, no significant variations of ξ are observed in the 70-, 100-, and 130-nm-thick BCP films with increasing Φ.