A silicone rubber composition comprising (A) a normally liquid organopolysiloxane having at least two silicon atom-bonded alkenyl radicals, (B) a liquid organohydrogenpolysiloxane having at least two Si--H radicals, (C) a blend of two inorganic powders selected from three highly heat conductive inorganic powders which form 30% slurries at pH at least 8, 6 to less than 8, and less than 6, and (D) an addition reaction catalyst cures into a silicone rubber having a high thermal conductivity and heat resistance and is suited for fixing rolls or belts in copiers.