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.
(..) Don't turn your back on me, Scar. On, no, Mufasa. Perhaps you shouldn't turn your back on me. Is that a challenge? Temper, temper. I wouldn't dream of challenging you. Pity! Why not? Well, as far as brains go, I got the lion's share. But, when it comes to brute strength... (..)1994 The Lion King