He 'tempered' his criticism 'with' a few words of encouragement. = He 'tempered' his criticism 'by' adding a few words of encouragement.
He was upset but 'kept his temper'. [=remained calm; did not become angry, begin shouting, etc.]
Higher interest rates have 'tempered' [='lessened'] the demand for new houses.
(..) we find that he is not so simple. That he wanted women violently... but stayed tied to the apron of his wife. That he lived in constant rage... but lost his temper only once. That he was a man of massive size and frame... but wore waistcoats, lace and gloves. So that by the time (..)1974 The Gambler