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.
(..) You know that. Your father... ...my brother, we were opposites. We would fight and argue. But I never doubted his love. He would do anything for me. But his temper... Too much. It clouded his reason. I don't want you to make that mistake. Also... ...he, too, had a way with women. (..)1990 The Godfather Part III
(..) - Just trouble. I'll take care of it. - That's foolish of you. Foolish of me? It's a little foolish of this guy, don't you think? Right? - Right?! - Temper like his father... Vincent... Mr. Joe Zasa now owns what used to be the Corleone business in New York. You took it against my advice. (..)1990 The Godfather Part III