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So can someone actually explain how we know that; let's say, exactly 116,342 years ago it wasn't half a degree hotter on average that year?
I get the global trends for hundreds of years to average out a general baseline of how temps were, but what is being tested or checked that say even 130 years ago the everage temp wasn't warmer that year? It seems like this 12 months being the hottest is more like an educated and informed guess than an actual fact.
There are scientists who study ice cores. Every summer a bit of ice in the north pole melts exposing liquid water to the air and interacting with it. Every winter that liquid freezes again. What we are left with are layers of ice that have been frozen in different years. These layers go back thousands of years. With our knowledge of atomic physics, we know what kind of isotopes exist in the atmosphere at certain temperatures. With this knowledge we can calculate the temperature of the earth in years past. We can also measure the amount of CO2 in the atmosphere that was present in the past. With this information we have found the is a direct relation to the temperature of the earth and the amount of CO2 present in the atmosphere.
I am sure someone can explain this better than me, but this is the jist of it.
If it only exposes liquid water in the summer then it's not recording a full year's worth of interaction, seems like a pretty foundational flaw in their method.
As with any proxy methods, they are verified with some other proxies that can be linked directly to reality. For example dendroclimatology - we study tree trunks to see how trees developed over years and we know how that connects to climatological conditions. We don't have hundreds of thousands of years of tree data, but we have enough to verify ice cores. And there are many, many more verification methods like that (for example records of weather phenomena in historic sources). And then all of that is connected in climate models, which can join that data from different sources and which can be again verified in multiple ways.
And even the ice cores themselves are not as simple as ice melting, as there's for example snow that falls every year and gets compressed.
So while climatology is not my favourite science discipline, with the amount of verification and validation they do, I have no problem with trusting climatological findings.
Also, due to winds, currents, and unknown weather patterns from thousands of years ago, you aren't getting an average temperature from across the globe where that ice sample is. You're just getting information from those few months in that area.