In this study the onset of stress-free Boussinesq thermal convection in rotating spherical shells with aspect ratio η = rinner/router = 0.9, Prandtl numbers Pr ∈ [10−4, 10−1], and Taylor numbers Ta ∈ [104, 1012] is considered. We focus on the form of the convective cell pattern that develops, and on its time scales, since this may have observational consequences for thermonuclear burning and the development of burst oscillations in the exploding oceans of accreting neutron stars (Watts (2012)).