The themal diffusivity has been ivestigatedin double perovskite Sr2MMoO6 (M=Fe, Mn and Co) by means of the mirage effect. We have found that the thermal diffusivity of metallic Sr2FeMoO6 is 0.39 cm2/s, wihich is larger than that (0.33cm2/s) of insulating Sr2MnMoO6 and Sr2CoMoO6. We further investigate the substitution effects of the La3+ions for the Sr2+ions in Sr2FeMoO6 and Sr2MnMoO6, and have found that the thermal diffusivities of both samples significantly increase with the La cncentration. Such an enhancement of the thermal diffusivities has been a scribed ot occupation of the extra itinerant electrons on te conducion Mo4d band.