We already have a world of migration. The news is filled with articles of 'refugees' being forced from here to there. Usually these stories are filled with human suffering. Resentments build as poor people in the home country are 'forced' to accept poor people from 'over there' and to provide the resources necessary for survival.
War might not be the first consequence of these developments, but will certainly follow close behind other effects. As the problems of global warming become more and more pronounced, they will join with existing problems of poverty, hunger and depletion of natural resources and will drive everything to the breaking point.
The world is dominated by greedy and stupid governments that will be unable to maintain themselves. These governments have already proven their inability to deal properly with ethnic & religious populations. They also fight over mundane issues. It will get worse. To compensate, governments will gravitate more and more into 'police states' in an effort to preserve themselves. Government leaders will loudly shout patriotic statements attempting to rally people to their cause. Nationalism will be accelerated.
But, national borders will have less meaning under the emergency situations of global warming and wars will be the result. There will be wars over water rights as rivers are gobbled up by one country at the headwaters, leaving downstream countries with a dry riverbed (think of the Colorado River). Many of the wars will be civil wars where neighbor fights neighbor for the meager resources available to feed one's family.
In other places, climate change is real. Some island nations, including the Maldives, are already considering the relocation of their entire population.