I saw the show you are referring to. What they claim would happen is the icebergs/ice caps would melt. That would decrease the salinitiy of the ocean. The decreased salinity would then cause the 'converyor belt' effect of the oceans, which cause the gulf stream to recirculate, to either slow down, or stop altogether. This recirculation helps to moderate temperatures around the globe (in conjunction with the prevailing winds) and dicking with it would cause the temperatures to go all out of whack.

That was the scientific conclusion, anyway.