https://history.aip.org/history/climate/index.htm
I'm not familiar with the details of the scientific findings, but AFAIK, there are several different significant factors involved in the warming & cooling of the earth.
The factor that's most important NOW is human society's emissions of "greenhouse" gases that affect how much of the sun's incoming radiation is radiated back into space, and how much of it remains in the lower atmosphere to cause "global warming.
Another very important factor TODAY, from what I've read, is the "algedo" or reflectiveness of the Earth's surface and of the clouds in the upper atmosphere. The place where this is urgently important, according to many climate scientists, is the Arctic circle.
There the polar ice cap, because it's white, normally reflects most of the sun's energy that strikes it back into outer space. This helps to keep the planet cooler. But as the Arctic region has warmed over the past 25 years, the size of the ice cap in the summer months has shrunk dramatically. White, reflective ice has given way to darker green or blue sea water, which absorbs much more of the sun's incoming radiation.
This decreasing "albedo" -- this decreasing reflectiveness -- of the Arctic polar region should cause the planet to heat up more quickly. It should step on the gas and accelerate the process of global warming.
3. But there are other factors involved in warming & cooling the planet as well.
a. One is the shape of the earth's orbit around the sun, which varies over a period of many thousands of years. At some times, the orbit causes more of the sun's energy to hit the Arctic polar region in the summers, which accelerates global warming. At other times, a changing orbit causes less of the sun's energy to hit the Arctic polar region in the summers, which can bring on an ice age.
b. The "tilt" of the earth on its axis also goes through a cycle of changes over many thousands of years. When the tilt allows more of the Arctic to be exposed to summer sunlight, this encourages global warming. When the tilt exposes less of the Arctic to summer sunlight, we have global cooling and we normally head into an ice age.
c. The intensity of the sun also varies over -- I think it's an 11-year cycle, which corresponds to the cycle of sunspots appearing and disappearing. More intense sunlight coming into the earth's atmosphere causes warming conditions; less intense sunlight causes cooling conditions.
d. The circulation of deep ocean currents, which can carry heat from what part of the earth to other parts, also affects global warming and cooling. That's why some climate scientists believe the climate was significantly changed when drifting tectonic plates caused North America and South America to come together at the Isthmus of Panama many millions of years ago. This changed the major ocean currents and changed the climate as well.
d. The weathering of mountain rocks by erosion has an indirect effect on climate because it removes carbon dioxide from the atmosphere, combines it with minerals in the rocks, and then causes the minerals with carbon attached to them to be washed downstream off the mountains into rivers, and from rivers into the oceans and the seas. Over millions of years, this causes carbon that used to be present in the atmosphere -- and that has caused global warming -- to become buried in deposits beneath the ocean floor. Which should cool the planet.
e. The big cycles of ocean currents that you mention in your question also affect the average warmth of the atmosphere. I don't know if they do so in the way the articles you linked to suggest. But since a great deal of the "global warming" that has happened from greenhouse gas emissions since 1850 has added heat to the oceans, not to the atmosphere or the land, how the big ocean currents circulate that heat has a big influence on what the climate of coming centuries will be.
-- democratic socialist / retired environmental journalist