From these definitions (1, 2, 3, 4) I have concluded that warmth is a facet that describes how much a person is showing warmth and love towards other people (e.g., touching, kissing, saying nice things) and empathy is how much a person sympathizes with the feelings of other people.
What if you are high in warmth but low in empathy? How would such a person behave? Isn't those facets are somewhat opposite of one another?