I make a point of removing myself from the situation if given the opportunity. Taking some time to process can help to cool things down.
I also find it helps to phrase everything more passively. I don't tend to say "you did this and that wrong," but instead say things like "unfortunately, mistakes happen, and that seems to be the case here," or something along those lines. Not a great example, but you'll find that careful phrasing can often help to avoid or minimize heated discussions.
Trial practice is confrontational by its very nature. But you pick up skills.
I'd recommend taking negotiations classes and getting on the moot/mock trial team if and when you get to law school. You'd certainly pick up tons of useful skills in there.
As we all know is to take time for deep breaths and remove yourself from any discomfort. There are loads of egos flyings around during the process of a case, such as upper management and opposing counsel. Take the words that they say as gospel and work with it and that should diffuse the situations that may lead to heated arguments. Appreciation of their viewpoint is also something you can consider. Also do your research first hand to avoid any complications with the case, which I am sure there will be in the more complex cases.
As to staying calm, try taking an acting class. Much of trial is theatrics. There should be few surprises by then. You don't always want to stay calm! Sometimes you want to be outraged or disgusted, but, just for a moment. You must be in total control of your emotions at all times!