what is the density current that carries warm water to Europe?

Answer 1

the Gulf Stream

Answer 2

The oceanic current that you're referring to is the Gulf Stream. However, the water is cooled and more dense (thus sinking) by the time it gets to Europe. The common idea that the Gulf Stream is the reason for Europe's mild weather is being questioned. See this recent article in the Scientific American:
http://www.americanscientist.org/template/AssetDetail/assetid/51963?fulltext=true

(And a note about the answer above mine. The density of water depends primarily on the temperature and salinity, which are variable throughout the ocean.)

Answer 3

The Gulf Stream is what does that, but I dont know what it's density is, I assume though that's it's the same of other salt water.