Get into American’s heart, not cold (5)
I believe the answer is:
enter
'get into' is the definition.
('enter' can be a synonym of 'get into')
I don't understand how the remainder of the clue works.
(Other definitions for enter that I've seen before include "Gain access to" , "Set foot in" , "Enrol" , "Infiltrate" , "Introduce" .)