His name kinda gives him away.
And heck, even the first mention of the Beast is all negative: he's a young prince who is "spoiled, selfish, and unkind," according to the narrator. He's actually not all that different from Gaston on that front and had he not been interrupted by a certain spell-wielding enchantresses, he might have grown up and been the same way. Luckily (or unluckily, depending on your point of view), he gets the magic whammy put on him in time to encourage a serious change in outlook.
How long is that magic whammy? Well, the narrator says that the magic rose will "bloom until his 21st year," giving him a chance to understand what real love is. Later, Lumiere tells us that "10 years we've been rusting." By using the power of math, we figured that the Beast is 11 years old when he does his Bearwolfalo thing, giving him plenty of hormonal-development time to think about what he's done.
And, we can assume that it helps…at least as far as giving him some humility. He's a little sensitive about his looks when we first meet him, and while he seems to treat his servants with more respect (something we suspect he wasn't doing back in his Little Lord Snotnose days), boy, does he have a temper. That scares the daylights out of the one girl who might get him out of this mess, and the help is terrified of him. Maurice is pretty much convinced that he's going to eat Belle with a nice Chianti and some fava beans.
So, yeah, anger issues.
And yet, that anger also means that he's on his way to better things. We catch him here at his low point, where he's feeling the most sorry for himself. His 10-year window is about to close. We don't approve of his lashing out, but we can at least understand the frustration that leads to it. In a lot of ways, the movie is about his learning to put that part of himself aside.
It starts by example.
Belle offers herself to the Beast in exchange for her father's freedom, an act that catches the Beast completely by surprise. "You! You would take his place?" he asks, genuinely shocked that anyone would do anything for anyone other than themselves. That, coupled with the more practical realization that this gal could allow him to comfortably hold silverware again someday, prompts him to take her out of the tower and into more comfortable chambers.
He follows her example almost instinctively when he rushes out into the snowstorm to save Belle. He was only a few minutes behind her, after all, and she was riding a horse at full gallop. Not a lot of time to think there, but off he goes regardless…suggesting that there's a good guy in there just waiting to come out. From there, he goes through a series of increasing steps where he learns to forget about his own needs and just make Belle happy.
In the end, he actually gives up Belle, restoring her freedom at the cost of remaining a walking shag rug forever. That's the completion of his journey, though he still has to wait until Belle realizes that she loves him and comes back. Even then, he demonstrates how much he's changed, sparing Gaston's life when he really has every right to snap the jerk's neck like a chicken bone and ultimately dying in Belle's arms with a final "at least I got to see you one last time."
If that's not a heart-melting moment, we don't know what is.
That movement from selfishness to total giving is the transformation of the Beast's soul—the only place where real beauty matters, the film assures us, and the thing he needs to understand if he's not going to end up becoming Gaston 2.0. And, there's more to that than just becoming a better person, though clearly he does that.
He suffers to do so, feeling every moment of the pain he's going through. At first, that suffering is focused only on himself as he wallows in self-pity. (Seriously, Beast? Not a thought for any of your servants who get to eat a big helping of your bad karma?) Then, it shifts to being separated from Belle, and finally, it gives way to grace and acceptance when he realizes that he's dying. Only then does he finally show what it takes to be a good man, just in the nick of time to revert to Squarejaw McHunkypants (personally, we think he looks like a young Brendan Fraser) and give us all a happily ever after.
Disney movies usually focus on the princesses more than the princes, but in this case, his is a pretty solid character arc: the redemptive story of a grade-A jerk who learns to care about someone else.
Talk about reforming the rake.