In a polydisperse thermotropic main-chain liquid crystalline polymer, we observe lie process of thermally induced nematic-nematic phase separation between short and long polymer chains. We study the dynamical features of this system, in particular the evolution of Schlieren textures Formed by disclinations surrounding areas of relatively uniform director. We analyze the dependence of domain size xi on temperature and the nematic order parameter, and the evolution of textures with the waiting time at a temperature well below the nematic transition T-ni. We End that: before phase separation the coarsening proceeds toward the uniform state, with characteristic size of the texture increasing as xi similar to t(1/4). When the system is phase-separated, the texture in the regions with long chains is frozen at an equilibrium value xi, a reversible function of temperature, while in the short-chain regions the coarsening accelerates. This behavior is interpreted in terms of a miscibility gap that is proportional to the degree of nematic order, which is different for the different lengths of the nematic polymers.