Warm water doesn't sink, cold water does.
Ocean currents are caused by density differences, which are caused by temperature (and salinity) differences.
Warm water is NOT being drawn down.
I don’t subscribe to this AGW crap, but an interesting property of water is that as the temperature decreases, there is a point where its density increase stops, then reverses. If I remember correctly, that point is 39*F.
So technically there is a window close to the freezing point where the warmer water will sink.
But the AGW theory is still crap.