Something about this line of discussion tickled my memory, and eventually i refound and reread this paper from 1978

Climatic Change, v1, issue 4, (1978) pp349-354

Ferren MacIntyre., "On the temperature coefficient of PCO2 in seawater"

" ... one ancillary problem can be disposed of quickly. This is the speculation that raising the surface temperature of the Earth a little will, by warming the oceans, force enough additional CO2 out of solution into the atmosphere to result in a runaway positive feedback. The idea is not implausible, but the numerical value of the temperature coefficient commonly quoted is far too large. "

The key insight is that the calculation must be done holding total C in ocean + atmosphere constant.

"It appears that fears of positive feedback in ocean-atmosphere warming were exaggerated ten-fold by a thermodynamic misunderstanding. For once, Nature seems to be on our side. "

MacIntyre neglects the deep ocean, which is ok for his treatment for timescales no more than a century or so.

Nice paper.

To return to the point that models include these considerations, Fig 12.42 and 12.43 in IPCC AR5 WG1 make the point explicitly for longer term (until 2300) projections, long tail even in RCP 2.6 with negative emission tech.

And IPCC points out that:

"Due to the long time scales in the deep ocean, full equilibrium is reached only after hundreds to thousands of years"

far beyond any projections.

sidd