A simple dynamic model is developed for the investigation of the hohlraum symmetrization by estimating the time changes of the optical geometry of the components under the influence of hohlraum radiation. The expansion of the converters heated by ion beams is also included. By performing dynamic simulations of the hohlraum target, it is found that the change in hohlraum geometry due to hydrodynamic expansion has a crucial effect on symmetrization. It is also found that the symmetry is now strongly dependent on time, and the optimal condition can only be satisfied for a limited time interval. An improved version of the hohlraum target is discussed, which may considerably increase the optimal time interval. This concept includes the suppression of the dynamic expansion by using low-Z gas in the hohlraum, the reduction of the optical expansion of the converter by using low-Z material, and modification of the shield configuration.