With the rate of warming slowing the big numbers in Ocean Heat Content (OHC) pops up as a diversion. Those big numbers, Joules times 10^22 are based on temperature change from an estimated "normal" total OHC. The data for the OHC estimates is spotty at best even with the ARGO float system that started in 2002. The depth of the OHC estimate is now down to 2000 meters or about half of the ocean volume. On the bright side, since deep ocean temperatures are so stable, the confidence intervals are very small because nothing much changes, temperature wise. Capacity wise, the numbers are big because the mass of the oceans is in the ballpark of 1.4 time 10^21 kilograms. With everything based on surface temperatures and energy flux, throwing Joules time 10^22 in to the mix can get confusing.
Luckily, NOAA also has the deep ocean data in plain old temperature.
This chart has the hemisphere deep ocean temperature anomaly compared to the Hadley version 3 sea surface temperature. They are adjusted to a common 1955 to 2012 baseline and I have added a scaling factor of 5 for the large differences in the anomalies. That is just eyeball scaling so don't try to get to crazy with make more of the chart than is there.
As I have mentioned before volcanic forcing impacts the NH more strongly than the SH. The NH ocean heat capacity is discharged more quickly, not hard since the average NH SST is 3 C greater than the SH, and the SH thanks to the Antarctic Circumpolar Current just keeps transferring energy north until things get rebalanced. Once the NH recovers from the volcanic cooling, then the oceans can start either warming in unison or do the seesaw thing. The temperature change for the deep oceans during all this is pretty small and takes a long time. Six hundreths of a degree per 33 years, if that is an "average" rate of gain, would be 0.18 C per century or about 444 years per every 0.8C of deep ocean warming. That would mean it would take about 1700 years for a 3.06 C increase in deep ocean temperature at that rate of gain.
As I said, the "average" is kind of important since the oceans tend to like the 4 C average temperature with the ACC on the job keeping the NH about 3 C warmer than the SH. Since the NH and SH can have nearly equal temperatures with the same 4 C deep ocean you could have a +/- 1.5 C swing around whatever that "average" temperature might be. How that +/- 1.5 C change in "average" SST translates to the "average" surface temperature could be anyone's guess, but since most of the ice sheets are gone, it is pretty unlikely that there is a great deal more warming in the "pipeline".
Since the deep ocean temperature scales pretty well with the surface temperature, I will leave with this little chart of past Indo-Pacific Warm Pool SST using the Oppo 2009 data.
It still looks to me like "most" of the warming is not due to CO2 unless CO2 depletion caused the last Little Ice Age.