in a heartfelt way vs dearly

in a heartfelt way and dearly both are adverbs.

Word	Noun	Adjective	Verb	Adverb
in a heartfelt way	No	No	No	Yes
dearly	No	No	No	Yes

As adverbs, in a heartfelt way and dearly are synonyms defined as:

in a heartfelt way (adverb)	dearly (adverb)
in a sincere and heartfelt manner	at a great cost
	with affection
	in a sincere and heartfelt manner