warm to somebody/something ( also warm up to somebody/something American English ) phrasal verb ( see also ↑ warm )
1 . to begin to like someone you have just met:
Bruce didn’t warm to him as he had to Casey.
2 . to become more eager, interested, or excited about something
warm to a theme/subject/topic etc
The more she spoke, the more she warmed to her subject.
Voters are starting to warm up to the idea.