Graft copolymers of rigid-rod polymers, specially synthesized for single-component molecular composites, were investigated by wide-angle X-ray scattering. The copolymers consist of a flexible poly(ether ketone) (PEK) side chain attached to a rigid-rod poly(p-phenylene benzobisthiazole) (PBZT). Emphasis was especially placed on the extent of rod aggregation in the copolymers before and after heat treatments. Results were compared among the graft copolymers of various structural characteristics and the blend of PBZT and PEK homopolymers. The results confirmed that the flexible side chains effectively suppress the thermally induced rod aggregation. The frequency of the graft sites along the rigid-rod backbone was found to be the key structural parameter limiting the extent of rod aggregation. A certain minimum frequency of the graft sites appeared to be required for the copolymers to be stable against the thermal aggregation. The side-chain length showed only a minimal effect, while the rigid-rod backbone length exhibited no effect on the stability of the copolymer morphology in association with the thermal aggregation.