So just to get this straight, the warming up of the Gulf Stream is leading to colder temps.
You see, this is where your stupidity is really coming to the fore.
Now, what happens when warm water meets ice?
Now what would happen to that warmer water, if you added colder water to it?
So, let's ramp the temp up 5 degrees. Would this happen quicker, or slower?
The gulf stream will simply drift more southerly, as the body of water it's child currents drift into, gets colder, which will lower the temp of the sea, forcing the gulf stream and it's children, lower, and cooler into to warmer areas. This leads to wetter, colder weather here.
The part you are getting confused with, is that you think the gulfstream dissipates when it hits this colder water. It doesn't, it shifts, which is why we would get weather change.
Is it really that tricky to understand?
The waters in the Mid Atlantic, on Monday, were reported as 3 degrees down on average temps. And look, hey, wetter weather, colder weather. Coincidence? Maybe. Sign of the future? Maybe. I don't know, as I am not a climatologist, nor meteorologist but I do know logic and the forcing of the Gulfstream south, something we have, for generations, relied on for our temperate climate, seems to indicate our climate will change too.