Jim
You misunderstand me. I invoke Milankovitch cycles for the timescale on which the surface cools, not for the timescale of ocean currents. Ocean currents are irrelevant to the timescale on which the direction of heat transfer changes.
Heating requires that the object being heated is colder than the object doing the heating.
The only reason water coming up now is colder than water going down, is that the surface has recently warmed. Its not always the case that water coming up is colder. Its only the case that water coming up is colder when heat is being transported down. On whatever timescale the surface eventually cools, the water coming back up will become hotter than the water going down, and thats when heat comes back out.
Simple box model.
Surface water at temperature Ts. Deep water at temperature Td. Flow between them w. Deep water mass Md, and residence time td=Md/w. Specific heat capacity of water C.
Heat transfer from surface to depth = wC(Ts-Td)
To get heat transfer from depth to surface requires Td>Ts
The main driver for changes in Td is this heat transfer.
wC(Ts-Td) = MdC dTd/dt
(Ts-Td)/td = dTd/dt
For Td to increase requires Ts>Td and this can't happen until whatever is driving Ts drives Ts back down. (Ts-Td) will approach zero on the timescale of td but it can't go negative unless something else takes Ts down. You take your pick of driving mechanisms, I took Milankovitch, and whatever timescale that operates on is the timescale on which the heat transfer reverses.
This sort of box model is decent for long term trends. The way I interpret the paper that inspired this thread in box model terms, is that the exchange rate, w, varies on a decadal timescale, and thus Ts increases at slower rates in the decades when w is high, and higher rates when w is low, despite a constant increase in radiative forcing.
If what is meant by heat coming back to bite us is that there are both El Ninos and La Ninas, or noise comes in above trend as well as below trend, then fair enough. However, heat coming back out of the deep ocean won't change the trend, it will never amplify the trend, all it will do is moderate the trend when something else causes it to reverse, just as it is currently moderating the upward trend.