With the self-similar solution of X-ray confinement in cavity, the time-dependent redistribution of thermal X rays inside the hohlraum is calculated. Distribution of radiation power intensity on the capsule's surface is calculated via the view-factor method. After that, the time-dependent radiation drive symmetry of the capsule could be studied. The effects of motion of laser spots, laser pulses and pointing error of capsule on the radiation uniformity are analyzed. Multi parameter couples are scanned to reach the minimum of time-integrated value of the second coefficient of Legendre polynomials. The best lengths of hohlraum agree with the results of implosion symmetry tuning experiments on SG-II and SG-III prototype laser facilities. The best length-to-diameter ratio of hohlraum is close to the point design targets on the National Ignition Facility (NIF). The validated model may give some reference to the future experiments design and analysis of implosion symmetry.