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.
(..) Piss off, you nonce. Santi. You given up that little nurse for Jordana? What did you say? You going to show your Mexican temper? - Come on, leave it. - Yeah? Yeah? Don't get me wrong. I'm just saying. Is it true? Did you fly all the way down here for this? (..)2007 Goal II: Living the Dream