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.
(..) Well, if you hadn't frightened me, I wouldn't have run away. Well, you shouldn't have been in the west wing. Well, you should learn to control your temper! (GRUNTS) Try to get some rest. Thank you, miss. We are eternally grateful. Why do you care (..)2017 Beauty and the Beast