warm or warm up
1.I feel cold at this moment and I want you to come to warm me or warm me up?
2. the party has just warmed up----does it mean that the part has just turned actively?
In sentence 1, it would be I want you to come warm me up.
In sentence 2, yes you are right, the party has just warmed up means that the party is just beginning to get fun/exciting/active.