He is a man at heart.
I love a man at/by with heart.
Are they two correct? Which types of prepositional phrases are they? I mean whether they acted as adjectival or adverbial prepositional phrases?
They mean nothing as written. They require more words.
He is a man who, at heart, is very nice. [essentially]
At heart, they love their children. [essentially]
at heart is an adverbial phrase that means essentially or basically because the heart in Western culture is the center of being. For example, the heart of the matter=the essence of the matter, the center of the matter.
Those are people with heart. [loving people]
at heart is basically adverbial and with heart is adjectival.