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.
(..) Excelsior! How'd a nice girl like you wind up working in a dump like this? Fella done me wrong. You got lousy taste in men, kid. He's not so bad. Well, he has a temper. Deep down he's all fluff. Fact is, he's not like anybody I've ever known. All my friends are fighters. Sounds amazing. (..)2015 Avengers: Age of Ultron