Among thermoresponsive hydrogels, poly-N-isopropylacrylamide gels are well known for their marked deswelling behavior near Tc ~ 32C; under slow, quasistatic heating, the gel shrinks affinely. In contrast, a rapid temperature quench above Tc produces an effectively impermeable outer skin that fixes the total volume of the gel, inducing the phase coexistence of solvent-rich and solvent-poor regions. For cylindrical gels, or gels characterized by a centerline with circular cross-section more generically, the simplest phase-coexistent scenario consists in having an axisymmetrically arranged, collapsed-outer region and an interior-swollen region, all centered along the centerline. Introducing a polarization vector to describe the solvent distribution in the phase separated state reveals that breaking axisymmetry lowers the system’s free energy. If the gel’s centerline is initially curved, this polarization couples to the local curvature and tends to point opposite to the normal vector of the centerline, thereby biasing the phase separation process. This coupling generates a feedback loop: curvature influences polarization, and polarization in turn drives further shape change. Interestingly, in the cylindrical case, a spontaneous polarization lowers the free energy, which then induces the bending of the cylindrical gel by the coupling between polarization and deformation. Finally, we show that cylindrical gels of different diameters quenched above Tc also exhibit other size- and temperature-dependent instabilities.