@hyportnex The situation you suggest (an unstable equilibrium analogous to the Rayleigh-Bénard instability), if it would result from the setup I described, would indeed answer my question. Do you suggest that there would be an unstable, no-flow situation?

@AtmosphericPrisonEscape thank you for the suggestion (2); I had not thought of expansion. Presumably at some degree of expansion, we will lose as much heat to radiation as we gain from the heating, and so there is no energy source for further expansion, which would store gravitational potential energy. At this point, then, we are faced with the original question. Perhaps this results in a spherically symmetric temperature gradient with no convection, and this system is in an unstable equilibrium? Where, as hypnortex suggests, a perturbation would lead to the formation of cells.