Hello again
Thanks for your follow up! No, that claim is not true. The numbers sound impressive until you factor in the volume of the whole ocean. 
I count around 113 nuclear power plants that are on a coastline. That includes plants that are currently operating, plants that are closed, and plants that are being built. (see the map here)
A typical plant discharges warm water at a rate of 90 cubic meters per second, and the temperature differential is between 5.5 and 7.5 degrees C. (source).
90 cubic meters/sec adds up to be 7,776,000 cubic meters/day, which is 0.007776 cubic kilometers per day. For a whole year, that would be 2.8 cubic kilometers, and multiply that by the number of plants - let's use 100 even though there are fewer than that operating, and you get 284 cubic kilometers per year.
OK, now let's compare that to the volume of the ocean, which is 1,335,000,000 cubic kilometers. (source) (Your estimate was incorrect - mostly because there is no such thing as a cubic ton, so it's hard to know what that number was referring to.)
So 284 is quite a bit smaller than 1,335,000,000. In fact, the discharge water is equivalent to 0.0000002 of the ocean volume. Those are the two numbers one needs to compare if you want to measure the impact of nuclear cooling water on the ocean temperature. The added heat does dissipate to the atmosphere, especially since it's discharged on the surface, not at depth. 
The math simply does not work out. It's not possible for water coming from nuclear power plants to influence the ocean temperature one way or another. The numbers don't add up.
If you wanted one more line of evidence, you can look at geography. All but a handful of nuclear power plants are in the northern hemisphere. If we look at a map of where the ocean has warmed, we should see more warming closer to the sources, and then we'd see that dissipate as the water flows away from the sources.
But that doesn't match the observed warming of the ocean, which you can see here is actually much more prevalent in the southern hemisphere. 
I hope that helps resolve your question. Thanks!

- NASA Climate Web Team