Cold-heartedly tells you how an action was done: in a way that shows no pity or sympathy. He cold-heartedly turned them away. The meaning is the same as cold-hearted, but this form hangs on the verb, not on the person. It is not a word you need every day. The adjective cold-hearted is the one people reach for first; this adverb turns up in writing, or when someone wants to press on the cruelty of the act itself.