The reason you're worried about this is that you haven't crunched the numbers. Sure the chart looks worrisome. Here's the wikipedia version (if you want the peer reviewed sources for this, click around and you'll easily get them.)
So the change in heat is about 2x10^23 Joules over a period of around 20 years.
The global warming folks tell us that the real global warming problems begin when we get the earth's temperature to rise by 2C. So let's use that as our temperature. Now they're worried about a 2 degree C change over the next 100 years or so which is 100 = 20x5 or 5x longer than the 20 year rise shown above. If the ocean heat continues to rise at the above rate, we're talking about a heat increase of about 5x(2x10^23) = 10^24 Joules = 1,000,000,000,000,000,000,000,000 Joules.
That's a lot of heat. One of the things alarmists like to do is to use units of "Hiroshima bombs". I think this is a rude disrespect but we can do the conversion as they never bother to do it for this situation. One Hiroshima bomb is about 6x10^13 Joules or 60,000,000,000,000 Joules. Doing the long division, we find that the energy stored in the oceans over the next 100 years is about 1.7x10^10 Hiroshima bombs or 17,000,000,000 bombs, that is, 17 billion Hiroshima bombs and the amount stored in the last 20 years was about 3 billion Hiroshima bombs.
Over the course of a century, all that heat will be distributed over the entire oceans. But just for the moment, let's see how much water we can heat 2C higher using 10^24 Joules. Of course if the heat is used exclusively to melt ice, or to evaporate water, the temperature will change by nothing (if you think otherwise, try learning a little thermodynamics, the subject here is a "phase change") but let's make the worst case assumption that the heat is absorbed by liquid water which stays liquid.
Turns out it takes 4.1813 Joules to raise the temperature of 1 gram of water by 1 degree C. Thus it takes twice this or about 8.36 Joules to raise a gram of water by 2C. And so the 10^24 Joules are enough to raise about (10^24)/8.8 = 1.2x10^23 grams of water by 2C. Converting to kilograms this gives 1.2x10^20 kilograms of water.
So what percentage of the oceans will we have raised in temperature (over the next 100 years) by 2C? It turns out that mass of the world's oceans are about 1.4x10^21 kilograms. This is about 12x larger than the amount of water that will be increased in temperature by 2C. And if we are to warm all the world's oceans by those 2C, then, at the present rate, it's going to take about 12x those 100 years.
So the final result is this:
If the CO2 heat goes into the oceans, it will take about 1200 years to warm the oceans by 2C.
If I were a betting man, I'd say that fossil fuel usage drops to near zero *before* those 1200 years go by.