When you give someone your "heartfelt thanks" it means that you are thanking them in a very deep, geniune, emotional way. This is a rather formal phrase that you can use when giving a speech, writing a formal letter, or making a public announcement.
There are a few ways to use "heartfelt thanks" in a sentence. Here's one – "my/our heartfelt thanks to ___":
Our heartfelt thanks to everyone who participated.
Here's another – "give ___ my/our heartfelt thanks":
I give you my heartfelt thanks for everthing that you've done for me over the years.
Other words that you can use with "hearfelt" include:
- my heartfelt apologies
- our heartfelt condolences