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.
(..) - Let him go. Hold on, hold on. Maya - I said let him go What are you doing? - ccs, a dose half of this size and I'm dead It's times like this my temper is tested somewhat Maya, give me the injector. If I die Killian, what happens to your soldiers? What happens to your product? (..)2013 Iron Man 3