A practical experimental method is proposed to investigate thermal transport by characterizing the motion of plasma flows through a x-ray spectroscopic technique using tracers. By simultaneously measuring multiple parameters, namely, the mass-ablation rate, the temporal evolution of plasma flow velocities and trajectories and the temperature, it is possible to observe a variety of physical processes, such as shock wave compression, heating by thermal waves, and plasma thermal expansion, and to determine their relative importance in different phases during the irradiation of CH and Au targets. From a comparison with hydrodynamic simulations, we find significant differences in the motion of the plasma flows between CH and Au, which can be attributed to different sensitivities to the thermal transport process. There are also differences in the ablation and electron temperature histories of the two materials. These results confirm that velocities and trajectories of plasma motion can provide useful evidence in the investigation of thermal conduction, and the approach presented here deserves more attention in the context of inertial confinement fusion and high-energy-density physics.