After my temper wears off, it feels a little like I'm waking up with a hangover. What did I do? What was I thinking? How am I going to clean this up? Even if I didn't literally turn into a green monster, it wasn't that far off. I got the destructive, overreactive, babbling idiot part down pretty good.
The Gemara in Nedarim (22) says that when a person is angry all kinds of hell overpower him. הסר כעס מלבך והעבר רע מבסרך Remove anger from your heart and remove evil from your flesh (Ecclesiastes 11). And the Gemara says רע (evil) also refers to Hell. A person literally suffers greatly, even physically when he's angry. But that doesn't stop him. Its one of the wonders of being human.
Anger really comes from the sense that one's personal desires or vision for what should be is the ultimate authority. When things don't go your way... Hulk Smash!! But we're not talking about an unusual kind of delusion. In fact, there's a good reason to feel this way. One of the words for soul, נשמה, is called a "portion of G-d above" That means that one's deepest desires and sense of self-worth come from an extremely holy place and demand great respect. The catch is, one only has access to that holy place by recognizing he is placed in the world to make a positive influence, and not to gratify oneself or make oneself worshipped. (Just to be clear, of course, in no way does this mean a person is G-d by virtue of his soul. G-d created souls and is prior to and beyond them)
The Holy Zohar says that when a person gets angry, his connection to his נשמה, his higher source of self, is replaced with something called אל זר, a "foreign god." The full meaning of this is beyond us, but there is something we can take away. False gods are called "foreign" because they are "foreign" to their worshippers. They seem on some level to satisfy a need, but ultimately leave the worshipper empty handed and disconnected, feeling a stranger to his own life. Anger brings this kind of power into the world.
We think that by getting angry we can force our will and claim our position of authority. Many times we fail, and even when we get our way, we don't get love or respect. On the contrary, we look silly, lose respect, and create distance. The Gemara Kedushin (41a) says רגזן לא עלתא בידו אלה רגזנותא "An angry person is left with nothing but his anger." We become strangers to our "worshippers" and to ourselves when we choose anger over relationships.
The opposite of anger is called סבלנות, which literally means the ability to carry a burden (and weakly translates as patience). It's holding onto a personal sense of what-should-be, together with the reality that there is another person here, with their own psychological infrastructure and their own baggage, or a situation that's more involved and complex than you want it to be. As opposed to being a stranger, סבלנות is using your lofty sense of self to be a positive influence and work with a complex world.
One way that Jewish wisdom could suggest integrating סבלנות is to meditate on the phrase I mentioned above, "An angry person is left with nothing but his anger." Consistently, a few minutes a day, say it out loud until it fits naturally on your lips, and reflect on what it means to you, how anger hurts you and how things could be better without it. In addition, when you feel yourself getting angry, recall these words of wisdom and your reflections. Through this process you can become more aware of how anger feels when it starts coming up and what makes you angry, until it becomes less and less common and you become more of a "carrier."