The translation is more like, "Day by day, it is getting warmer, isn't it?" The warm part is 暖かい (あたたかい). First, the "to become" verb termination, なる is added and conjugated: あたたかくなる (to become warm). The きました here is actually the past tense of くる (to come). You would combine the two verbs あたたかくなる with the くる by conjugating あたたかくなる to its て-form: あたたかくなってくる, before conjugating this "compound verb" あたたかくなってきました. So in Japanese, the literal idea is more like: Day by day, the "becoming warm" has come.