Under normal conditions the heated equatorial regions of the planet are moderated by a northward current flow in the Atlantic Ocean which in fact warms the UK, Scandinavia and indirectly nearby parts of Europe. The water becomes cooler and is subsequently warmed again by flowing back southward down along the African coast and then back around through the Indian Ocean where it helps regulate monsoons that come to India and Southeast Asia. Afterwards these currents circle back along the equator making complex loops into the South Atlantic and the Antarctic and into the Pacific Oceans and then repeats the circuit. This is complex circulating current known as the Thermohaline Conveyor Belt.
The current flows are affected by the water density which is altered by cooling or warming temperatures and as well by sudden influxes of fresh water. In the past, specifically near the end of the last ice age, it is thought that these currents were interrupted by a huge flow of fresh water from land ice sliding into the sea–somewhere between Northern Canada and Greenland. The details are not known, but the outcome was the disruption of the Thermohaline Conveyor Belt current and a relatively sudden transformation of the weather in Europe and Scandinavia which went back into ice age like as well as initiating drought conditions in Eastern Europe. If something this were to happen again we would see similar effects in Europe and Scandinavia as well as changes in the Far East due to failures in the Monsoon Rains.
No one expects a release of significant waters into the Atlantic like those which appeared near the end of the last ice age, as those waters have already gone, and while the Greenland Glacier is melting slowly it would have to rapidly accelerate and move into the Ocean far more rapidly that it appears to be doing presently. If that were to happen it would take quite a while to disrupt the northern branch of the Thermohaline Conveyer Belt Currents. Then, in addition as they did toward the end of the last ice age heat would move by some mechanism off the equator and preferentially into the South latitudes–eventually warming the west Antarctic ice shelf and sending much of it into the sea. These effects (losing both a major piece of the Greenland glacier and the West Antarctic ices shelf) would raise sea levels and threaten many of the cities that are now developing very large populations. Before mid century we should have nearly 30 such mega-cities, and nearly two thirds of those would be underwater should the equivalent of the Greenland glacier and the West Antarctic ice shelf fall into the sea.
While major regions of North and South America would be spared many of these devastating effects of Thermohaline Conveyer Belt disruption and sea level rise with the exception of several of the cities noted above being underwater. Europe and Scandinavia would experience an immediate crisis while Asia and the Far east would have serious issues as well including drought but without a near ice age.