Eefs, no suggestions on the work situation, but here's what I do to avoid the crying thing...
For me, if I can afford to kind of tune out the person ranting, I do the primes in my head (1, 3, 5, 7, 11, 13....) or sometimes multiplication by 17. Anything where I can half listen, but also have something else going on in my head.
Or this past weekend when I was very angry with the hospital and needed to keep calm and remember I was right, I kept saying to myself "I am a wall, I am a wall." As it somehow fit but was such a bad analogy, I had enough on my mind (yes, it was a really bad analogy) to dismiss the doctor's tone and inference that I was a neglectful mother.
If I were you (and, of course, I'm not, but maybe this will inspire something?): I'd also write down, point by point, my comebacks to every single thing in his letter and keep them on my person. For me, writing things down and having them on me is enough for me to remember in times of crisis. I don't think I'd want to pull them out to check.
Also, if he's ranting and you're tuning him out (after first figuring out the proper response -- usually they will give the key to the proper response first, then go on and get all ranty), wait for him to finish and do not interrupt and then wait (ie count slowly to 5) to respond. Ranters tend to fizzle out and get thrown off when people don't rant back.
Think of an out and go by what he said in his note. Lead him on and bring the points up yourself. If you've got the answers, you can handle the questions.
And, this has been my trump in these sorts of situations: apply the phrase, "It's not what you say, it's how you say it." Don't be argumentative, be slightly confused about the complaint with a tad of wondering about how this man could be so stupid.
My husband thinks I'm nuts with the wall thing (and probably with the primes), but that is my first defense against crying. The rest is, honestly, just manipulative bullshit, but has been effective for me.
Again, I've never been a corporate person, but these things have worked for me here and there and I'm hoping you do well tomorrow.
My husband just read this and suggested getting a performance review from your supervisor and also seconded (thirded? fourthed?) talking to HR.