By now most have seen this exchange. Supposedly it showcases McCain's temper but it seems relatively tame to me.
McCain has long been known to have a flashy temper. In my opinion he's a little too hot-headed for the job all things considered, but then again so is Hillary (which is probably why they get along so well). I'd prefer a more even-tempered individual but as to whether it's a showstopper, it's kinda too late based on the choices still left.
While he might have a temper, I don't think he's dangerous in that regard, and he'll have plenty of advisers in the White House to bounce off his decisions. The downside is the hot-head reputation possibly affecting future decisions due to political calculations designed to thwart the image. That is, if he can get to the White House with the temper reputation.
The bigger story here might be the press. Everyone knows McCain has a good relationship with a press that votes 85 percent Democrat, but rational observers would say it was mainly because the Maverick would occasionally inspire warm fuzzies by going against his own party. Elizabeth Bumiller's pseudo-smarmy "why are you so angry" comment should open his eyes to a new reality, highlighted in many of the press accounts of the event that convicted McCain in their headlines.
But surely he must be aware of this. Surely he must know they will try to bait him into a meltdown to get a story. If he doesn't he's not smart enough to lead the country. And if he does, yet still cannot control the temper or make a strategic plan to thwart or explain the negative stories (such as an appeal directly to the American people) well, ditto.