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.
(..) I think I can see the appeal. No. What? Why? I checked the Psych evaluations. He's far too unstable. He's trying to say, that he has a temper. Have you any idea what we'd be putting him through? The psychological strain requires someone emotionally balanced. We have to be scientific. (..)2014 RoboCop