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.
(..) Once. (Song: I've got a dream) *I'm malicious mean and scary.* *And violence-wise my hands are not the cleanest.* *But despite my evil look, and my temper and my hook.* *I've always yearned to be a concert pianist.* *Can't cha see me on the stage performing Mozart.* *Tickling the ivories, (..)2010 Tangled