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.
(..) 'but to be safely thus! 'Our fears in Banquo stick deep.' And in his royalty of nature reigns that which would be feared. 'Tis much he dares and to that dauntless temper of his mind... (SWORD SCRAPES GROUND) ...he hath a wisdom that doth guide his valour. How now, my Lord? Why do you keep alone? (..)2015 Macbeth