Let's see. Well, 'well-being' refers to a person's overall mental, physical, and emotional health. 'At heart'-I understand that to mean that the other person's well-being is her top priority (the most most important thing to her).
I'll give you another example: "The boss had his employees' well being at heart. So, even though he wanted more money for his company, he didn't force his employees to work long hours." (The well being of his employees was his top priority-more important than making more money.)