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.
(..) want to see us both headless. My sister is likely to say something provocative. And? And you've been known to lose your temper from time to time. - As all our great leaders do... - When have I lost my temper? Burning the Tarlys for instance. That was not impulsive. That was necessary. (..)2017 TvShow: Game of Thrones Title: Beyond the Wall Season: 7 Episode 6