Is the ocean guaranteed to warm in a warming climate? More specifically, I've seen some discussion of this article: 
http://www.realclimate.org/index.php/archives/2006/09/why-greenhouse-gases-heat-the-ocean/
which claims that the observed ocean warming is explained by the ocean skin absorbing long-wavelength radiation. What I am asking is: is this mechanism necessary for ocean warming to occur? 
My naive understanding was that our increasing the magnitude of the greenhouse effect meant that there was less radiation escapting to space, and therefore the average temperature of the entire ocean+earth+atmosphere system will increase until it reaches a new equilibrium, where outgoing radiation again equals incoming. Is this correct? And if it is, does it not imply that the ocean must also get warmer, simply because it is a thermally coupled part of the entire warming system? 
I had someone tell me that the a warming atmosphere could not warm the ocean, because the atmosphere has a much lower heat capacity. But it seems to me that the constraint on the final equibilibrium temperature means that all components must warm, no matter how inefficient the means of energy transfer between them. Am I right, or have I misunderstood? 
To clarify, I'm talking about an idealised earth that actually can reach equilibrium, and I'm ignoring all the complexities of ocean currents and winds etc. I'm just asking about the absolute thermodynamic basics. 
 A: As the comments suggest this is a subject for earthscience.SE. Here I will say that what warms the earth, and any planet, is primarily the input energy from the sun, primarily because there also exist volcanic energy at some  ratio. 
If one posits a fixed incoming energy, then the mechanisms of how this energy is distributed, ocean bulk, ocean surface, land , reflection back to space are a matter of a complete dynamic model of a complicated chaotic system.
This article gives an idea of the complexity , the factors that enter to describe a dynamic system.

But it seems to me that the constraint on the final equilibrium temperature means that all components must warm, no matter how inefficient the means of energy transfer between them

Well , a dynamically chaotic system is never at equilibrium . In the sense if one takes average values for everything, there would be an average temperature for the ocean surface and the land masses and the atmosphere , but the ocean would be heated by the direct incoming radiation and not by contact with the atmosphere  which would be a smaller contribution, exactly because of heat capacities.
Hotter currents heat the atmosphere as is know by the Gulf stream:

The Gulf Stream, together with its northern extension towards Europe, the North Atlantic Drift, is a powerful, warm, and swift Atlantic ocean current that originates in the Gulf of Mexico and stretches to the tip of Florida, and follows the eastern coastlines of the United States and Newfoundland before crossing the Atlantic Ocean.

.....

The North Atlantic Current of the Gulf Stream, along with similar warm air currents, helps keep Ireland and the western coast of Great Britain a couple of degrees warmer than the east.[28] However, the difference is most dramatic in the western coastal islands of Scotland

