Animal-hearted: when a person identifies as human but has a strong "connection with" or feels a "relation with" an animal. The term was coined on The Daemon Forum. It's definition was clarified by a member named Teddy on October 26, 2009.
"I identify WITH wolves." does not have the same meaning as "I identify AS a wolf." Being a Therian is more than "really liking" an animal. Liking a creature a lot does not equal an identity as that creature. Some people may use the term Kith. The equivalent term in the Otherkin community is Other-hearted.
To use the term correctly, a person who feels close to deer would say, "I am deer-hearted."
There is a thread on AHWW from January 15, 1997 in which someone who claimed to "ABSOULUTLY ADORE WEREWOLVES AND WOLVES" asked if they were "wolfhearted".  The term animal-heart was discussed more thoroughly and came into common use between 2009 and 2010. 
The Daemon Forum - http://daemonpage.com/forum/index.php
Mossland "Animal-hearted Links" March 15, 2018 http://atlas-of-mossland.tumblr.com/post/171901555989/animal-hearted-links (Archived Page https://web.archive.org/web/20180326005327/http://atlas-of-mossland.tumblr.com/post/171901555989/animal-hearted-links )
Mossland "Common Themes in the Early Animal-hearted Scene" January 26, 2018 http://atlas-of-mossland.tumblr.com/post/170158667209/common-themes-in-the-early-animal-hearted-scene (Archived at https://web.archive.org/web/20180326003413/http://atlas-of-mossland.tumblr.com/post/170158667209/common-themes-in-the-early-animal-hearted-scene )
[Something]-hearted vs Therian, Werelist, March 14, 2010. http://www.werelist.net/archive/index.php/t-27515.html
- Mossland, "An Interesting Find" January 19, 2018 http://atlas-of-mossland.tumblr.com/post/169890816504/an-interesting-find (Archive Page https://web.archive.org/web/20180326003910/http://atlas-of-mossland.tumblr.com/post/169890816504/an-interesting-find
- House of Chimeras, August 17, 2014 "The History of the Term Animal-Hearted" http://liongoatsnake.tumblr.com/post/94999217300/the-hisotry-of-the-term-animal-hearted (Archived page https://web.archive.org/web/20180121005409/http://liongoatsnake.tumblr.com/post/94999217300/the-hisotry-of-the-term-animal-hearted )