Is it allowed in Islam to like a girl in your heart but not to hang out with her?

All perfect praise be to Allah, The Lord of the Worlds. I testify that there is none worthy of worship except Allah, and that Muhammad is His slave and Messenger.

Loving a specific girl could be in two forms:

1) To love such a girl due to suddenly seeing or receiving some information about her. Here, if one loves this girl in his heart, fears Allah, and avoids seeking any forbidden thing from her such as making appointment, exchanging letters, looking at her, etc., then there is no blame on him. Also, there is no objection to make every permissible effort to marry this girl, if possible.

2) To love such a girl because of one's own choice, will and effort. Such a case is like the one who does not avoid looking at a woman and considers such an action as normal. So, he exchanges letters and glances with women. This, as a rule, is completely prohibited in Islam due to its bad consequences and violations of the Sharee'ah.

Allah knows best.