The values of the externally applied thermal gradients that give rise to uniform liquid layers of a ternary deuterium–tritium mixture inside a cryogenic spherical shell inertial confinement fusion target are calculated using a model recently developed by the authors. It is shown that the surface tension gradients induced by the component separation at the liquid–vapor interface pull the liquid upward, thus counteracting the gravity-induced fuel sagging and forming dynamically stable uniform liquid layers. The governing equations are the equations of continuity, momentum, energy, and mass diffusion–convection, which are solved using finite-difference methods. The solutions indicate that one needs fairly large positive thermal gradients, obtained by keeping the top of the target warmer than the bottom, in order to create uniform liquid layers on the inner surface of the target.