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.
(..) lt was nice to see you. The thing is, with you l'm in real... danger. lt seems like a... perfect situation, apart from that foul temper of yours, but... my relatively inexperienced heart would, l fear, not... recover, uh, if l was... once again cast aside, as l would absolutely expect to be. (..)1999 Notting Hill