The idea that global warming will produce global cooling is counterintuitive to many people, but that process of heating leading to cooling is a basic part of the 'orbital theory' of an insolation-driven (sunlight-driven) Ice Age cycle. The 'orbital theory', which is based on the fact that cyclic changes in the earth's orbit of the sun alter the amount of sunlight that reaches the earth, is the leading theory of Ice Age causation.
It is likely that the next Ice Age will be preceded and precipitated (literally) by an upward spike in global temperatures and warming of the oceans, which will increase oceanic evaporation and cause an increase in global precipitation, some of which will fall as snow, that will feed the growth of glaciers at high latitudes and high elevations.
An Ice Age is characterized by the formation of vast glaciers on top of large continental land masses. Since there are much larger continental land masses located in the high latitudes of the Northern Hemisphere than in the Southern Hemisphere, it is in the Northern Hemisphere that the Ice Age cycle is most obviously manifested. At the peak of the last Ice Age glacial maximum, about 17,000 years ago, glaciers up to two miles thick covered all of Canada, Scandinavia, and most of Britain.