In the last 12 months, the 0-700 m region of the ocean has gained 1.5 W/m2 of heat**, and the 0-2000 m region 1.7 W/m2.
That's a gain of 25 ZJ (zettajoules) for the 0-700 m region, and 28 ZJ for the 0-2000 m region. (By way of contrast, "...mankind generates 0.5 zetajoules of energy every year in its power stations.")
An acceleration of 0.10 W/m2/yr sounds large to me -- what forcings are, in total, increasing at that rate? -- but that's what the data says.
* NOAA ocean heat content data: 0-700 m, 0-2000 m.
** The area used here is that of the entire Earth, since about 93% of the GHG-trapped heat goes into the ocean.
*** Yes, heat may be increasing, or decreasing, below 2000 meters. I'm aware of this paper, which finds a small increase of 0.05 W/m2 for the region below 3000 m for the 1990s and 2000s. If you know of additional studies on the deep ocean, I'd appreciate if you left them in a comment.
**** The basic statistical error bar here (two-sigma) is ±0.03 W/m2/yr. I don't know how to include autocorrelation in a 2nd-order polynomial fit. If you can help me out with that, let me know. Thanks.