1 billion years ... that's older than both plants and animals ... ice caps have come and gone, hell, the oceans at the equator were solid ice within the past billion years ... and Antarctica was temperate like the United States just 30 million years ago (3% of a billion), no ice at sea level a'tall ...
There will be life on Earth ... it won't be human life is all ... "the Homo branch of the Tree-of-Life is putrid and diseased and will die and fall off" ... just tasting bad doesn't help as much as photosynthesis would ... but I digress ...
Heat exchange is predictable ... not sure why you think it's "notoriously" unpredictable ... there are three laws governing energy as it moves through the environment ... they never fail ... not even a counter-example ... they work perfectly in chemistry, biology, classical physics, geology, oceanography ... and Atmospheric Science ... they're just difficult to understand and apply ... but give satisfactory results nonetheless ...
This idea that CO2 is a major factor in climate change is faulty and has been debunked over and over. It's just like the flat-earth theory from just 500-600 years ago. The faulty and hysterical reaction is to "lower carbon footprint". Instead of thinking we can somehow change the climate by destroying our energy economy, we should be expanding our efforts to create real solutions to our changing weather patterns like diversifying food crops and animals, providing stable water supplies, and moving populations out of harm's way where necessary. But since the leaders of the world are embarking on this quest to kill carbon, the thing life itself is based on, civilization is likely to fail and we will no longer be able to tackle the civil projects that would save us. So yup, it very well may not be humans inhabiting the Earth.
This has happened before in history. The great civilization that spanned Mexico & Central America went through a climate change. Instead of figuring out ways to grow their crops (like creating aquifers), they turned to ritualistic sacrifices to appease their gods. This situation today is no different: the leadership wants to sacrifice carbon to appease their faulty idea that it will change the climate.
Here is a graph depicting the recent increase in Atmospheric CO2 (most likely caused by the increasing amount of life on Earth as the arctic tundra becomes more active):
And here is a graph of the average hi and low temperatures from a nearby weather station for about the same time period:
As you can see, there is no correlation between the steady rise in CO2 and temperature.
Furthermore, the change in Atmospheric CO2 is only 0.02% between pre-industrialization and today. It is absurd to believe this small change could cause a significant change in global temperatures. The energy transfer phenomenon the hypothesis is based on is not a catalytic phenomenon: the effect that CO2 could have is directly proportional to its physical composition in the air. Here is what the cause and effect chart looks like:
The green speck in the bottom left is an approximation of the percentage of the effect we now would have at 0.042% total atmospheric CO2. In the worst case scenario, we can estimate that the percent of the effect now in play is somewhere around 0.05%. Now, we do not know exactly what the resulting global temperature change would be if we went from 0% CO2 to 100% CO2. But pick any number. Let's pretend you said the global temperature would be 100 degrees F higher. If that were the case, then the current effect of CO2 would be to increase temperatures by about 0.05 degrees F.
Even this analogy is incorrect. The actual effect of increasing CO2 would be to block the sun's energy from reaching the earth, thereby lowering global temperatures.
Maybe God will grant the next species that takes over the Earth better reasoning skills.