I need to find a thesis for an oral essay on F451. We are given a quote by Socrates to guide the essay. It is as follows: "The unexamined life is not worth living."

Now, I've tried to get more specific into this quote, but I don't feel I'm getting anywhere. Here are two that I've written, and scratched out already:
1) An unquestioned life is one covered by a mask of happiness and denial, and is not worth living.
2) Unconscoiusly, every person strives to be unique in their life, but it is only when one conscoiusly examine's one's life and lives for themself, that one finds true happiness and meaning in it.

Personally, I believe the second attempt is leading me somewhere, so maybe you guys can lead me to a better thesis from that. Any other ideas would be appreciated! Maybe you guys can link themes of denial, ignorance, and self-destruction to the above quote.

Yes, but did Socrates really exist? Nothing he ever wrote exists! Everything attributed to Socrates comes from the writings of Plato, Aristophanes, and Xenophon, as well as Antisthenes. Many think Socrates was actually the creation of Plato. THAT in itself would make an interesting thesis.

By the way, the second suggestion you posted is the one to go with.

Would it be good if I talk about how those characters in Fahrenheit 451 that examine their own life reach a satisfying state (e.g. Montag, Faber, Clarisse), and those that are unable to realize their unhappiness do not (e.g. Mildred)? What else could I write about? Any would be greatly appreciated!

I think you're on the right track. If, however, you decide to use your "no. 2" above as an introductory statement, be careful not to have your pronouns in disagreement (or disarray), i.e, "...examines one's life and lives for oneself...".
By the way, it's not a bad idea, you know, to challenge the axiom; for instance, Mother Theresa was so busy noticing the needs of those around her and taking care of them that she had little time to "examine her life". Yet, hers was certainly "a life worth living". Just a thought.
Good luck!

Actually, there is pretty good evidence that Socrates existed. he is the subject of the play by Aristophanes and is referred by other writers. If just a figment of Plato's imagination, the play and other references would have been about Plato. In the Platonic catalog, one of the fun pursuits is in determining where Socrates ends and Plato begins. But there are some points of consenses as to where differences exist that can be identified as Socrates, and others as Plato. Very fun stuff. This gray area exists, but I'm not familiar with a lot of serious scholarship that doubts Socrates was a real person.