Lower
者 supplies the sound — zhě shifted to shǔ through Old-Chinese palatal alternation. Same phonetic in
暑,
署 government office,
著 to write,
煮 to boil,
薯 yam — a tight zhǔ/shǔ family.
者 here carries no agent-suffix meaning; it is a pure phonetic loan, useful for predicting summer-heat-related characters share this sound peg.