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.
(..) Yeah, that's right. I know stuff. Grover! Enough! I can't take this anymore. It's been two days! Calm your temper! Calm your temper! I haven't had a decent meal since those half-bloods you brought! And this stupid fleece is supposed to lure satyrs! (..)2013 Percy Jackson: Sea of Monsters