The Gulf Stream indeed contributes to Europe's warmth, but it is wrong to conflate the climate difference across the North Atlantic with the northward flow of warm water in the Gulf Stream. This erroneous logic leads to such statements as (from The Times of London): "The British Isles lie on the same latitude as Labrador on the East Coast of Canada, and are protected from a similarly icy climate by the Atlantic conveyor belt." Such claims are absolutely wrong.

This certainly changed my understanding and also Al Gore's.

American Scientist Online - The Source of Europe's Mild Climate