Warm towards
Definition 1 of 1
Pro Tip 1/3Emotional Change
Indicates a shift in feelings from neutral or negative to positive and friendly. 
Despite her doubts, she warmed towards the new neighbors after their kind gesture.
Pro Tip 2/3Gradual Process
The phrase often suggests the development of positive feelings is happening slowly over time. 
He gradually warmed towards the idea of adopting a pet.
Pro Tip 3/3Not Instant
'Warm towards' is rarely used when someone likes another immediately; it's a progression. 
After a few meetings, she finally warmed towards her colleague.