Isochoric heating of matter by intense heavy ion beams promises to become a fruitful approach to warm dense matter studies. For heating times that are long on the hydrodynamic time scale of the target response a tamped target is essential. The proposed dynamic confinement provides homogeneous target heating by a low-Z tamper, which allows one to apply powerful x-ray scattering diagnostics. To demonstrate the potential of the method, heating of a hydrogen sample with the SIS-18 beam at GSI Darmstadt is investigated numerically. The intense x-ray bursts for diagnostics can be provided by the PHELIX laser currently installed at GSI. In the optimized heating regime, density variations can be reduced to a level of 15% from the initial density value.