In a manner that lacks kindness, sympathy, or warmth; in a way that shows no care for others' feelings.
From coldhearted plus the adverbial suffix -ly, indicating manner or how an action is performed. This adverbial form allows the adjective quality to modify verbs and other adjectives.
Adding -ly to describe how someone acts ('coldheartedly rejected') versus just describing them ('coldhearted person') is a subtle shift in English that moves the focus from their character to their behavior.
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