I have read a bunch of stuff like this... where it seems that the heat goes from the ocean to the air... but not much the other way.
http://eesc.columbia.edu/courses/ees/climate/lectures/o_atm.html
Solar Radiation: Much of the direct and diffuse solar short wave (less than 2 micros, mostly in the visible range) electromagnetic radiation that reaches the sea surface penetrates the ocean (the ocean has a low albedo, except when the sun is close to the horizon), heating the sea water down to about 100 to 200 meters, depending on the water clarity. It is within this thin sunlit surface layer of the ocean that the process of photosynthesis can occur. Solar heating of the ocean on a global average is 168 watts per square meter.
Net Back Radiation: The ocean transmits electromagnetic radiation into the atmosphere in proportion to the fourth power of the sea surface temperature (black-body radiation). This radiation is at much longer wavelengths than that of the solar radiation (greater than 10 micros, in the infrared range), because the ocean surface is far cooler that the sun's surface. The infrared radiation emitted from the ocean is quickly absorbed and re-emitted by water vapor and carbon dioxide and other greenhouse gases residing in the lower atmosphere. Much of the radiation from the atmospheric gases, also in the infrared range, is transmitted back to the ocean, reducing the net long wave radiation heat loss of the ocean. The warmer the ocean the warmer and more humid is the air, increasing its greenhouse abilities. Thus it is very difficult for the ocean to transmit heat by long wave radiation into the atmosphere; the greenhouse gases just kick it back, notably water vapor whose concentration is proportional to the air temperature. Net back radiation cools the ocean, on a global average by 66 watts per square meter.
Conduction: When air is contact with the ocean is at a different temperature than that the sea surface; heat transfer by conduction takes place. On average the ocean is about 1 or 2 degrees warmer than the atmosphere so on average ocean heat is transferred from ocean to atmosphere by conduction. The heated air is more buoyant than the air above it, so it convects the ocean heat upward into the atmosphere. If the ocean were colder than the atmosphere (which of course happens) the air in contact with the ocean cools, becoming denser and hence more stable, more stratified. As such the conduction process does a poor job of carrying the atmosphere heat into the cool ocean. This occurs over the subtropical upwelling regions of the ocean. The transfer of heat between ocean and atmosphere by conduction is more efficient when the ocean is warmer than the air it is in contact with. On global average the oceanic heat loss by conduction is only 24 watts per square meter.
Latent Heat: The largest heat loss for the ocean is due to evaporation, which links heat exchange with hydrological cycle (Fig. 4). On global average the heat loss by evaporation is 78 watts per square meter. Why so large? ItÂs because of the large heat of vaporization (or latent heat) of water, a product of the polar bonding of the H2O molecule, as discussed in the Ocean Stratification lecture. Approximately 570 calories (2.45 x 106 joules) are needed to evaporate one gram (kilogram) of water! A gram of water is roughly one cubic centimeter, amounts to a loss of one centimeter of water per a square centimeter of ocean surface area. The water vapor leaving the ocean is transferred by the atmosphere eventually condensing into water droplets forming clouds, releasing its latent heat of vaporization in the atmosphere, usually quite remote from the site of the evaporation, thus representing a significant form of heat transfer, later heat transfer.
The annual heat flux between ocean and atmosphere (Fig. 5) is formed by the sum of all of the heat transfer process: solar and terrestrial radiation; heat conduction and evaporation. While the ocean gains heat in low latitudes and losses heat in high latitudes, the largest heat loss is drawn from the warm Gulf Stream waters off the east coast of the US during the winter, when cold dry continental air spreads over the ocean. An equivalent pattern is found near Japan, where the Kuroshio Current is influenced by the winter winds off Asia. It is in these regions that the atmosphere takes over as the major meridional heat transfer agent.