1.Prepositional phraseIn spirit; according to one's beliefs, views or feelings; deep down, fundamentally, really.
"I’m a vegan at heart – the thought of the death of animals for my food is abhorrent.; My dad may be old on the outside, but he’s young at heart; he plays video games every now and then to improve his coordination."
2.Prepositional phraseWished earnestly for; held in high esteem.