This is the overview I was working with 30 years ago:
The ocean is stably thermally stratified. There is minimal radiative or conductive heat transfer between the mixed layer and deep ocean. Transfers of heat between the surface and the deep ocean must be accomplished by mass transfer. This mass transfer is accomplished by geostrophic flow, thermohaline circulation, breaking internal waves, and biological mixing.
Geostrophic flow along continental boundaries causes upwelling and downwelling when the boundary currents cause offshore or onshore flow of the surface waters. The density of the water is relatively unimportant, the surface water is moving under Coriolis force. If it moves away from the coast upwelling replaces it, if it piles up on the coast it forces the water under it down and away. Upwellings, like the Humbolt current, cause cold, deep, nutrient-rich waters to come to the surface. Downwelling mixes warm water deeper than it would under surface influences alone. "Deep" here may mean as much as a km or 2 locally on very steep continental shelves with an offshore trench, but is typically less than a km.
Thermohaline circulation occurs when fresh water is removed from surface waters. The resultant increased salt concentration makes relatively warm water dense enough to sink through cooler water. This can occur in surprisingly hot water near desert coastal lagoons. The big thermohaline circulators, though, are the formation of North Atlantic Deep Water and Antarctic Bottom Water. NADW forms when Arctic ice formation removes fresh water from the surface layer, making it denser but no cooler. This dense water carries its heat deep, cascading down past the continental shelf. In the Weddell Sea, the lack of any warmer water to sit above it means that the NADW lies at the surface. Once again surface freezing makes water saltier and denser and it flows downhill becoming AABW - the deepest layer of water in the ocean. Formation of NADW and AABW are the only known large-scale mechanisms for moving heat into the deep ocean beyond a km or two - that is to say most of the deep ocean volume.
Breaking internal waves and biological mixing were both known to allow mixing past the thermocline (100 meters or so deep) when I was actively doing oceanography. They're much better understood now, and I believe that vertical diurnal movement as well as deep diving surface breathers are being realized as important biological mixing processes.
Heat also enters the ocean through its floor from the heat of earth's core. You can get some idea how little by noting that measuring this heat required thermistors 10 meters apart stuck into bottom mud to give a recordable signal with 1970's tech.