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.
(..) In three hours he'll be released with our proposition. Listen to what he has to say before you do anything. What's done is done. Don't lose that famous temper of yours, Sonny. I'll wait. Your boss is dead. I know you're not in the muscle end of the family, so don't be scared. (..)1972 The Godfather