Funnily enough the water temperature is why many are so focused on the arctic sea ice. It is acting as a buffer that is keeping large parts of the ocean cooler beyond both reflecting sun light and also actively melting and releasing cool water into the ocean.
But as it is shrinking rapidly, there is an eye being kept to see when we hit a "Blue Ocean Event". That is coverage less that 1 million sq KM as that is effectively gone as far as functionality goes. Only 15 years ago this was thought to be something that might happen in the 22nd century, it looks like we might see this in the next decade.
You can test the impact of this at home. Get a glass of water and put some ice in it with a thermometer. Once down to temperature, the water won't change much as the ice will melt to keep the temperature stable. But as soon as it is all gone, the temperature will start to rise rapidly. This is because of Latent heat fusion. The amount of energy it takes to change ice to water.
The amount of energy it takes to break the bonds of ice at 0c to into water at 0c, is the same about of energy need to take that 0c water up to 71c. When the arctic is gone, we lose a HUGE buffer on global temperatures.
It's like boiling a cup of water vs an Olympic sized swimming pool. The latter is going to take a lot more energy than the former.