Yes I commented this on somewhere else, but let's make a new blog comment conversation about it:

Ok so ima go through her entire personality and my interest by episode. You can just skip to my analysises, since that's what your interested in:

Incendium: In "Incendium", she shows us, at first, that she is either very interested in having a boyfriend, or simply wants a reason to escape from her glass prison. When Jake appears and says that "prince finn" is interested in her, she perks up immediately, without knowing his personality or appearance. When she's released, she says she is "so happy" and immediately hugs the fake finn that Jake has created from his body, meaning she can have a sweeter side, but when the citizens murmur that she "doesn't" seem evil, she becames enraged a shoots fireballs all around. When fake finn says he's not interested, she becomes very angry, meaning she has a deeper emotional side. She hates the idea of someone leaving her and decides to burn everything. She follows Jake and when finn holds her and says he likes her she is surprised, in a happy way at first, but then becames enraged. She is stubborn and would not like to embarras herself by making it seem like all her rage was for nothing.

My analysis: In this episode, I enjoyed her character because she was relateable and passionate, while also a little psycho, which is fun in a character (not in real life). No one wants to be wooed and then left immediately. She was so passionate about wanting a boyfriend, that she destroyed things when he left. I thought she was very cool in this episode, especially seeing her abilities. She threw fire, grew to a massive size, and we even saw that there is a real girl underneath her flames.

Hot to the touch: At the beginning, Finn does say that Flame Princess "ain't evil. She's just passionate." When the bird that has caught on fire flies over them, it is unsure whether flame princess did it for pleasure, curiousity, or revenge, but I doubt it was revenge because I don't see why the bird would provoke her. She is very curious when they spy on her. She doesn't seem to understand the world and begins burning small things like flowers. This is what evokes pity for many. She was locked away for so long that she doesn't understand the earth. Finn is madly attracted to her in this episode, calling her a "cute little flower". He tells her how he feels and her flame glows brghter. She is in much pain when he accidentally steps on her flames. She says that all he's done is hurt her, meaning that she does not feel like her actions were overexxagerations, and that she was very much offended and heart broken. She has spent her life, trapped, being forced to watch her evil citizens and developing their ways. It is, in no way her fault for her immoral personality. Finn gives her a deep speech about his feelings and she grows very bright and happy but is enraged again. She obviously holds a grudge and does not realize Finn isn't trying to torment or hurt her. Her psychotic side is especially shown in this episode. She burns down an entire civilization, while maintaining a normal disposition. She shows in the end that she likes Finn, and would like to date him, but nature wouldn't allow it.

My analysis: I enjoyed flame princess in this episode, because I saw a character, whom I already liked, develop. I saw that she was a little mad (as in crazy), which you have to be in wonderland. Whoops, I mean Ooo. I saw how much she cared of Finn's "like" for her and that his opinion mattered to her. I also saw that Finn likes her, which of course, is just shipping, but still cool to see that finn has a love interest who can and does like him back.

Burning low: Let's skip to the analysis

My analysis: Most of my love for her character in this episode is just her caring for finn. She is very happy when he is around and doesn't do anything psychotic. She even seems apologetic when she accidentally burns things, like his poem, whereas before, she didn't bat an eye. I simply enjoyed seeing her character develop into a more loveable person. Of course she still has all the great aspects that made FP fans like her to begin with, but she is sweeter. Finn says he got about 5 hugs when he went on his alone date, meaning she is passionate about him. In the end, it is very sweet that she is willing to compromise, and simply kiss the same rock together.

Ignition point and all the little people: Ignition point, she was more of a plot device but we still did see that she didn't want to go back to her kingdom and preferred the ways of finn and jake's world, and not her evil civilization. All the little people showed that she wanted to fight for finn, but it's not the most reliable episode.

Leave your thoughts, opinions, and analysises in the comments. Please add anything that I missed. These were simply my reasons for why I think flame princess is one of the most kick ass characters, and not just because she's dating finn. Some of it is about why I like that she's dating Finn, but there are reasons behind it. Anyways, thanks for reading. 

I have some edits:

In ignition point, I really thought she was one of my favorite characters. She wasn't in it much, but she had the coolest powers. We also learned that she could be turned good with a good guy (like finn), but there would be "penalties to her experience, if she acted out of alignment." I'm not exactly sure what that means, but perhaps, if she were turned good, it would change her elemental matrix. Just a thought. Could be wrong.

Worm King: Now, this was, of course, Finn's dream, but the personalities of the other characters did seem pretty accurate. In this, I saw that she was a persistent woman and tough. She wasn't in it, very much.

I have just learned that the penalties to her experience is a reference to Dungeons and Dragons. When acting out of alignment, players receive experience penalties. It may not have a deeper meaning.

All in All, I really like Flame Princess as a character because she really has a deeper core. She is relateable, yet fun and crazy. She is, as Finn said, passionate and I think that's great about a character. Deep below her fiery surface, there is a normal girl, physically and emotionally. Her passion for having someone who cares for her is grand. I enjoy watching her develop and seeing how much she cares, especially about Finn (Not in a shipping way, because she really likes someone good and has a very high chance of redeeming herself from her evil nature). In her most recent appearences, she seems happy and calmer which is great. But what I love about her the most is her powers. Seeing her grow to massive, fiery sizes, breaking apart into flaming pieces and reforming, igniting and destroying objects with fireballs and discs from thin air, and, my favorite, making a fake gun with her hand and blowing stuff up from far away.