Thick spherical shells, irradiated nearly symmetrically by ion beams, can convert efficiently ion beam energy to thermal radiation, with parameters of relevance to inertial confinement fusion. The evolution of such radiation converters has been studied by means of an analytic model, in turn validated by 1D radiation hydrodynamic simulations. Expressions are derived for the overall conversion efficiency, the heating time and the radiation temperature as a function of the beam and target parameters. Conditions are also derived for the effective hydrodynamic insulation between the converter and the fusion capsule contained inside the converter. For realistic heavy ion beam parameters (e.g. 6-8 GeV Bi beams, with total energy of 10 MJ and power about 700 TW) such converters can achieve an efficiency adequate for fusion applications, but only allow for a modest dynamic range of pulse shaping.