We have performed coarse-grained molecular dynamics simulations of thiophene-based conjugated oligomers to elucidate how the oligomer architecture, specifically the orientation and density of alkyl side chains extending from the thiophene backbones, impacts the order-disorder temperatures and the various ordered morphologies that the oligomers form. We find that the orientation of side chains along the oligomer backbone plays a more significant role than side chain density, side chain-side chain interactions, or side chain length in determining the thermodynamically stable morphologies and the phase transition temperatures. Oligomers with side chains oriented on both sides of the backbone ("anti") form lamellae, while oligomers with side chains oriented on one side of the backbone ("syn") assemble into hexagonally packed cylinders that can undergo a second, lower temperature transition to lamellae or ribbons depending on side chain-side chain interaction strength. The strength of side chain-side chain interactions affects the order-disorder temperature, with oligomers having moderately attractive side chains exhibiting higher transition temperatures than those with weakly attractive side chains. Side chain length modulates the spacing between morphological features, such as cylinders and lamellae, and affects the order-disorder temperature differently depending on oligomer architecture.