The refractive index of a liquid is known to depend strongly on the temperature gradient of liquids. When a laser beam passes through a transparent material going through thermal diffusion, the light projected onto a screen will be displaced in relation to the thermal diffusivity. A simple apparatus is used to measure the time evolution t of the laser beam displacement h and/vs. the position of the laser beam on the liquid container y whose liquid medium is going through thermal diffusion. Thermal diffusion dynamics can then be revealed. The thermal diffusivity of glycerol, ethanol, DI water, and NaCl aqueous solution has been measured. This simple procedure can demonstrate refractive index and thermal diffusivity in advanced high school physics courses.