The thermal diffusivity (alpha) of As20Te80-xGax glasses (7.5 <= x <=18.5) has been measured using photo-thermal deflection (PTD) technique. It is found that the thermal diffusivity is comparatively lower for As-20 Te80-xGax glasses, which is consistent with the memory type of electrical switching exhibited by these samples. Further, the thermal diffusivity of As20Te80-xGax, glasses is found to increase with the incorporation of gallium initially (for x <= 9), which is consistent with the metallicity of the additive, This increase in alpha results in a maximum at the composition x = 9; beyond x = 9, a decrease is seen in alpha leading to a minimum at the composition x = 15. The observed composition dependence of thermal diffusivity Of As-20 Te80-xGax glasses has been found to be similar to that of As20AsxTe100-x glasses, based on which it is proposed that As20Te80-xGax, glasses exhibit an extended stiffness transition with compositions x = 9 and x = 15 being its onset and completion, respectively. Also, the composition x = 17.5 at which a second maximum is seen in the thermal diffusivity has been identified to be the chemical threshold (CT) of the As-20 Te80-xGax glassy system, as at CT, the glass is configurationally closest to the crystalline state and the scattering of the diffusing thermal waves is minimal for the chemically ordered phase.