Abstract: The thermal diffusivity has been investigated in double perovskite Sr₂FeMoO₆ by means of the laser-induced transient thermal grating in the temperature range of 300~450 K.We have found that the thermal diffusivity of Sr₂FeMoO₆ shows a slow decrease in 300~360 K,and then decreases significantly around 380 K,which is the critical temperatureT_C for ferromagnetic to paramagnetic phase transition.We also find that the thermal diffusivity keeps a constant above 400 K.We further discuss the influences of phonon,spin and electron on the thermal diffusivity of Sr₂FeMoO₆ in different temperature ranges.