Good question:
Everybody assumes that World War III will be fought with nuclear weapons, but this may not be the case. It depends how we define it, but I think it's safe to say we are in a 'Global War'. Now when ISIS activates their sleeper cells across the world, conducting attacks against cities all at the same time all over the world, we may need to redefine it all, we know this is their plan and only a fool would ignore this possibility, especially with Europe and the US welcoming unknowns for a terrorist region with no vetting process whatsoever.
For now, i'd say we are in a global war on ISIS, and a cold war against Russia/China. Could change tomorrow, so stay tuned. We could go after ISIS in Syria (Or NATO) with troops, which can easily trigger a war with Russia. We can go from cold/global war to official WW3 in a matter of minutes under the right circumstances.
Since this question lies in the eye of the beholder, i'm going to say possibly.