The self-diffusion coefficient of sodium into β″-alumina doped with sodium oxide has been measured in the temperature range -45 to +18°. The measurements have been carried out into the same sintered material used in the sodium-sulfur battery where the β″-alumina is the solid electrolyte. The present study is a part of a programme of development of the solid state batteries designed in our laboratory which combine conducting polymers and solid electrolytes.