I don't know if Ulfric's temper would serve Skyrim well in such a difficult political period, where treading on the wrong toes at the wrong time could spell Skyrim's destruction.
Given the persistent notion that Ulfric is some kind of intemperate hothead, I'd really like to see specific examples of this that have actually been witnessed by players who interact with him. Because I've done the CW on both sides, have had just about every dialogue exchange that's possible with him in just about every situation, and I have yet to see any more or worse displays of "temper" than are put on by Balgruuf, for instance, or Tullius, and none of them were inappropriate to the situation at hand IMO.
For the most part, Ulfric comes off as a very deliberate, thoughtful, and "cool" character IMO. Where's the yelling, the screaming, the pounding on the table, all the stuff you'd expect to see on a regular basis from a character who some people keep trying to insist has "too hot" of a temper to be this or that or some other thing? It just ain't there, people, or if it is it's in some Bizarro Skyrim that I haven't discovered yet.