A "compassionate heart" means having a kind and caring nature towards others. It refers to a person who shows empathy, understanding, and helps those in need. Full definition
If you have a loving and compassionate heart for animals with a little extra room and time to spare, fostering a dog could forever change his life as well as your own. (dogcare.dailypuppy.com)
I have a lot of love to give and have a very compassionate heart. (singlesmeetonline.com)
Instead of promoting gangsters with attitudes, we can focus on creating decent citizens with compassionate hearts. (thedailyjournalist.com)