Solar evolution guarantees the Earth will experience surface temperatures hot enough to boil away the oceans. That will produce a run away global warming, but not for at least another 1 billion years. It is estimated that multi-cellular life has reached about the halfway point for viability on Earth,
Also, remember…water vapor mixing ratio follows ambient temperature. Water vapor acts as a powerful greenhouse gas to enhance any warming in an act of positive feedback. This feedback is partially mitigated by the negative lapse rate feedback concurrently induced (reducing greenhouse effect..net positive) and also by changes in cloudiness. Water vapor entering the atmosphere will not by itself cause a run away condition so long as an equal amount continues to precipitates out as what evaporates in.
In the deep past, climates warmer than 10C above current conditions have occurred. The climate system did not run away. Over the next several centuries humans stand to recreate the conditions of the PETM of 55 million years ago. The climate did not run away then either. Regardless of the global warming event we are currently immersed in (and causing), eventually the Earth will return to the climate conditions forced by the dynamic equilibrium between solar radiation and the Earth’s natural production of greenhouses gases.
As it just so happens, atmospheric CO2 content has fallen in step with the warming sun over the past several hundred million years. Good thing too, imagine how warm the Earth would be today if CO2 measured in parts per million were near 800ppm as they were during the period you refer to.
We are really just incredibly lucky to be here in the first place. The Earth just so happens to reside in a narrow region just the right distance from the Sun to sustain temps suitable for life and for water to exist near it’s triple point (gas, liquid, solid). We have a moon which stabilizes the Earth’s tendency to wobble wildly about it’s rotational axis. This is a major reason we have stable seasons on Earth. A few chance big asteroid impacts have randomly shaped the evolution of life on Earth. If any of of these and many more coincidences had not occurred we would most likely not be here. NO, we wouldn’t be here.
One of those chance happenings is that over the past several hundred million years CO2 levels have declined. Tectonic process involving mountain building and the positions of the continents, the amount of water runoff from the continents to the seas. The nature of life itself. The temperature, cooler conditions slowing chemical rock weathering in concert with all the above determine the amount of CO2 in the atmosphere. We are just lucky things have taken place just the exact way they have, including a period of low atmospheric CO2 coinciding with a warming Sun. If that had not been the case, the heat of the Cretaceous Period would have built even higher with the warming of the Sun, and who knows maybe the dinosaurs would have survived the asteroid to remain the predominant form of life on the planet.