Thermal diffusivity has been investigated in ordered double perovskite Sr2FeMoO6 by means of transient surface grating technique in the temperature range of 300-450 K. The thermal diffusivity shows an appreciable decrease from 39mm2/s at 300 K to 37mm2/s at 360K in the ferromagnetic phase, and then steeply drops to 10mm2/s with further increasing temperature above the critical temperature Tc ～ 380 K. Such an abrupt decrease of the thermal diffusivity has been ascribed to the structural phase transition at Tc. We further investigate the lattice effect on the thermal diffusivity in A2FeMoO6 (A = Ca, Sr and Ba) by substitution of Ca2+ or Ba2+ ions for Sr2+ions at 300K. We find that the thermal diffusivity increases from 35mm2/s for A = Ca to 41 mm2/s for A = Ba.Considering the change of the Fe-O-Mo bond angle from 152.4° for A = Ca to 180° for A = Ba, the increased thermal diffusivity for Ba compound has been ascribed to the enhanced hybridization between transition-metal d and oxygen p states due to the larger Fe-O-Mo bond angle and hence the wider one-electron bandwidth W.