We investigate dynamic director field variations in shells of the nematic liquid crystal (LC) compound, 4-cyano-4'-pentylbiphenyl, suspended in and containing immiscible aqueous phases. The outer and inner shell interfaces are stabilized by the cationic surfactant, cetyl trimethyl ammonium bromide (CTAB), and by the water soluble polymer, poly(vinyl alcohol) (PVA), respectively. PVA and surfactant solutions normally promote tangential and orthogonal alignments, respectively, of the LC director. The rather high Krafft temperature of CTAB, TK ≈ 25 °C, means that its solubility in water is below the critical micelle concentration at room temperature in most labs. Here, we study the effect of cooling/heating past TK on the LC shell director configuration. Within a certain concentration range, CTAB in the outer aqueous phase (and PVA in the inner) switches the LC director field from hybrid to uniformly orthogonal upon cooling below TK. We argue that the effect is related to the migration of the surfactant through the fluid LC membrane into the initially surfactant-free aqueous PVA solution, triggered by the drastically reduced water solubility of CTAB at T < TK. The results suggest that LC shells can detect solutes in the continuous phase, provided there is sufficient probability that the solute migrates through the LC into the inner aqueous phase.