A study published a little while back in Nature found an association between shifts in climate (in this case, shifts associated with El Niño) and international conflict. The researchers' hypothesis was that El Niño was messing with people's psyches and also creating economic shocks by tweaking food prices, dredging up storms, and fostering disease. These effects tend to make people a little testy and, boom!, conflict.
But, as Sarah Zielinski writes at Smithsonian, it's too simple to say that climate change will cause war: