We present a study of a phase-transition-driven separation in microemulsions of nanosized lyotropic inverse micelles and thermotropic liquid crystal pentylcyanobiphenyl (5CB) with 5%, 8%, and 15% micelle concentration. Using deuteron nuclear magnetic resonance (DNMR) microimaging in combination with conventional microscopy as well as ac calorimetry, we demonstrate a phase separation scenario in which micelles are expelled from the nematic phase during the I-N conversion. Due to a difference in density the micelle-rich isotropiclike phase spatially separates from the micelle-free nematic phase. A relatively sharp interface, formed between the two phases, can be controllably shifted by temperature-induced conversion between the phases. Once expelled, micelles do not remix into the nematic phase, whereas in the isotropic state their remixing takes place over several days. Temperature dependence of the linewidth of isotropic spectral component has been analyzed in terms of molecular reorientations mediated by translational displacements, assuming isotropically distributed directors of nanosized nematic domains. With our results, the existence of the proposed transparent nematic state cannot be completely ruled out. However, if present, the nematic order in such a phase must be extremely low.