*† Numerical results are presented for natural convection within a spherical enclosure using an hp-adaptive finite element technique. The time dependent laminar 3-D equations of motion and energy for an incompressible fluid are solved. The hp-adaptive model is based on both mesh refinement and increasing spectral order to produce enhanced accuracy while attempting to minimize computational cost. The 3-D hp-adaptive FEM code is first benchmarked by solving the natural convection heat transfer problem in a differentially heated cavity. Results are in good agreement with the literature. Natural convection is simulated within a sphere heated from below and cooled from above. Four recirculation cells initially develop during the early phase of the transient solution.