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.
(..) Anyway I hired my Dad, Max to maintain order as The Enforcer. Stratton very own Gestapo. We called him ''Mad Max. '' because of his hair trigger temper. Which could be set off by something as obnoxious as a ringing telephone. Who the fuck has the Goddamn ball to call this house on a tuesday night? (..)2013 The Wolf of Wall Street