The first step is admitting there is a problem.
Congratulations! I mean, it sucks having a short temper, but acknowledging the problem is still something to congratulate... considering how so many people out there still refuse to acknowledge any faults at all beginning with them.
I have been a bit of a punching bag most of my life as well, was bullied and ostracized most of my time in public school--yeah yeah, toughen up, I hear ya trolls. What keeps me from flaming out when I get insulted, or mocked, or what have you... is remembering all the times in the past, and even in the moment, it hurts me. I don't want to be treated like that... and that's exactly why I try to avoid treating anyone else like that. I'm in the unique position of knowing what it's like being on the side being put down. I know how horrible it makes a person feel... I know how bad it can make me perform in game, too. So, that's my largest motivator.
Don't get me wrong, I've had a message all ready to go. Angry caps, angry words, my blood is boiling, but somehow, every time, I manage to stop myself. Read what I wrote, shake my head, "it's not worth it. It is not worth it. Just play the damned game." And, let me tell you one of the best methods I've had for disarming the flamers and ragers and trolls... acknowledge what they say as fact, but play it off at the same time. "I know, Sona, I'm not doing great, but hey, you're playing with me!" "I dunno, Gragas, they seem to be camping me an awful lot... could just be that I need to ward more before i push out." But, really, the best thing to do is to... just not say anything. Shout at the air, scream and rant to your accepting friends, kick and flail in your chair like a petulant two-year old(I have done it, it helps sometimes...). If it's in the comfort of your own privacy, you're allowed to vent your rage and/or frustration in any way that is healthy to you. Don't let anyone else tell you what you can't do to vent, as long as it doesn't directly impact your game.
Hell, I've spent games talking back to people in my game, by just... talking at my screen. They can't hear me, I'm not streaming, no one else can really hear me--other than me. And it usually helps keep me cool. Because i'm getting it off my chest, in the most positive way I can manage to do it.
So yes, you can mute everyone and band-aid the problem... or you can try and find personal ways of dealing with it. What works for me, won't work for everyone, and what works for you, might not work for everyone. gg wp at the end of every game, even if you don't feel like it was a good game, or well played ... Humble in defeat, humble in victory. I shake my head everytime I see a "gg ez". Every. Single. Time. And yes, I report them for it. But that's my opinion, and no one can tell me otherwise. :3
And, sometimes, the best thing to do... is take a break. Play ARAM instead of SR for a few weeks(or SR instead of ARAM if you're an ARAM'er like I usually am). Try out a different game, maybe pick up a slower calmer game. Play two matches, then play your calmer game for 30 minutes or an hour. Then play another two matches of league, or three if you feel like you can handle it.
If you really feel like your temper is starting to become a problem, not just in League... there are therapists out there for this sort of thing. There is no shame in seeking professional help. Even I've seen a couple in my lifetime for a variety of reasons. And I don't doubt that someday in the future, I might have to see one again. (I am, unfortunately, becoming more and more anxious with each passing day, go figure.)
Well, this was a wall... hopefully I at least put something helpful in there. Flamers... COME AT ME! >:3 (oh, and cat smilies :3 help keep the grouchies away!)