We demonstrate that hot superheavy nuclei do not retain spherical shapes, as traditionally assumed, but instead equilibrate in deformed—often oblate or triaxial—configurations at finite excitation energy. This behavior arises from a mechanism analogous to the Jahn–Teller effect: spherical systems exhibit high single-particle degeneracy near the Fermi surface, causing their shell corrections to damp out significantly faster with temperature than those of deformed shapes. Using a finitetemperature framework, we reveal a thermally induced inversion of the potential-energy landscape in the Z = 118–120 region, where deformed minima become energetically favored at U ≈ 30–50 MeV. This shape inversion fundamentally alters the competition between neutron evaporation and fission. We derive a deformation-dependent correction to the survival probability, revealing a systematic bias in estimates based on spherical ground-state properties. Our results identify a finite-temperature structure effect that calls for a revision of current models of superheavy nucleus synthesis and decay.