The generation of thermal radiation by heavy ion beam heated cylinders, with parameters of relevance to indirectly driven inertial confinement fusion (ICF), is studied by means of 2D radiation hydrodynamics simulations and by a simple model, heuristically including the 2D effects. Scaling laws are derived for the conversion efficiency as a function of the beam and converter parameters and are found to be in agreement with the simulations for both a low-Z material (carbon) and a high-Z material (gold). The choice of the converter material is discussed