I think that, while it's entirely possible that, sometime in the next few decades, the world will be swept up in war, I don't think it likely that the government would christen it 'World War III,' if only to avoid the the negative opinions that such a name would stir up. We can leave that to the press.
"'But do you really mean, sir,' said Peter, 'that there could be other worlds --all over the place, just round the corner-- like that?'
'Nothing is more probable,' said the Professor..."
-The Lion, the Witch, and the Wardrobe