In shock wave technique, the shock wave velocity can't constrain the time-dependent radiation temperature because the shock wave breaking out time is not constrained. In this report, the time-dependent radiation temperature on Al sample can be inversed according to the shock wave breaking out time and velocity of Al sample combined with Bayesian inference analysis. This technique provides the uncertainty analysis of the time-dependent radiation temperature on sample, and obtains high-precision analysis results. The reliability of the inverted radiation temperature is fully verified by the experimental results of the burn-through flux in different energy bands and the burn-through spectrum of Al ablation sample. This technology involves simple physical process and single standard material Al. It can greatly reduces the influence of simulation and parameter accuracy on the analysis results. The precision inversion technique proposed in this report can be used to deduce the time-dependent radiation temperature on sample without destroying the hohlraum environment. It can be applied to various physical experiments of indirect-drive inertial confinement fusion.