A new version of indirect drive target is proposed for heavy ion inertial fusion (HIIF), in which the cavity for radiative symmetrization is filled with a low density low Z material and is called a 'hotraum'. When heated to a temperature T ⩾ 100 eV, the hotraum becomes transparent to thermal X-rays and ensures radiative smoothing of the energy flux which implodes the fuel capsule enclosed in the cavity. Ion beams are focused on the full target cross-section and deposit their energy in the high Z casing and in the outer region of the hotraum. The initial target configuration is spherical and requires no special orientation in the reactor chamber. Enhanced hydrodynamic efficiency of the capsule implosion, resulting from tamped ablation inside the hotraum, compensates for the high losses in the hotraum and leads to a beam-to-fuel energy coupling of about 5% and target gains in the range of 50-100. Hydrodynamic mapping of deposition nonuniformities onto the fusion capsule can be avoided by fast initial heating of the hotraum. A regime is found in which the ablating capsule insulates itself from hydrodynamic disturbances in the hotraum. The low density required for the hotraum fill allows stopping ranges of up to 100 mg/cm2, corresponding to 6 GeV 209Bi ions