At first he didn't know what would happen to him when he experienced heat (he has his own song about it called "In Summer"), but once he melted, Queen Elsa gave him his own personal flurry. Put him with summer and he'll be a happy snowman.
Aside from his happy funny side, Olaf also has a sweet and caring side. He built a fire for his friend Anna who was in danger of permanently freezing. Anna said, "Olaf! You're melting!" And Olaf replied with an original quote that will make history, "Some people are worth melting for."
* * *
Olaf: Hi, I'm Olaf, and I like warm hugs!
Adult Elsa: Olaf?
Olaf: You built me. Remember that?
Adult Elsa: And you're alive?
Olaf: Um, I think so...?
Then a serious fan of the show on one of the forums had a spaz moment and called the dragon OLAF. And it's been set in stone for us fandom people since.
Recently, people have also been turning OLAF into an Acronym for the dragon:
'Our Large Animal Friend'
An acronym within an acronym, to quote a paradox.
~Where Did The Dragon Go?
~Overly Large Acronyms for the Win