It's true that the ocean is vast and has a high mass -- 0.02% of the Earth's mass, in fact. It does not warm or cool easily. But:
a) that does not mean any change in its heat content is small, and
b) it certainly does not mean that the temperature changes by the same amount at all depths.
Exactly because the ocean is so massive, it takes a lot of heat to change its temperature -- in any region. Since 1955, the average temperature of the top 2000 meters of the ocean -- about 1/2 its average depth -- has increased by about 0.10°C. From the heat angle, that means the change in that region's heat content is about 300 ZJ (1 ZJ = 1021 J).
Exercise for the reader: compare this to the rate at which the Earth receives energy from the Sun, either at the top of the atmosphere or at the surface.
So who cares, right? Besides the question of the effect on marine life -- which I'm working on understanding, check back later, but let's point out that at equilibrium there will be little change at all -- what does this mean about the temperature change at various depths? It means it can still change by a lot by depth.
Using NOAA's data on ocean temperature anomalies and ocean heat content, we can calculate the temperature and heat changes in average regions. It's pretty simple; just recall that ΔQ = mc*ΔT (definition of specific heat). The data gives:
Put another way, here is the average temperature change as a function of ocean depth:
There's your thermocline. Calculating temperature change from changes in ocean heat content makes no sense unless you do it as a function of ocean depth.