How does heat get transported between the surface layer, twilight zone, and the deep ocean?
I think the simplest answer is through water mass formation, the resulting thermohaline circulation, mixing caused by wind predominantly in shallow regions, and through downwelling processes. The heat exchanged with the atmosphere in the surface layers determine the temperature of the near-surface water. From there, mixing (caused by wind, for instance) will transfer some of the heat to lower layers in the ocean. In the case of areas of water mass formation, the sinking of surface waters is usually enhanced. When the water masses are away from the ocean boundaries (surface and bottom), then the thermohaline circulation controls the transport and exchange between water parcels and thus the heat transfer.