warm up to
warm up to (someone or something)
To slowly begin to like someone or something. I'm not aloof, it takes me awhile to warm up to new people.
warm up to someone or something
Fig. to become more fervent and earnest toward someone, something, or a group; to become more responsive and receptive to someone, a group, or something. After we talked, he began to warm up to us a little. I warmed up to the committee as the interview went on.