But if you claim that this is the hottest month since then, when the average temperature varies by less than a degree a year, you’re implying that you know the maximum yearly average temperature from 120000 years ago to within a degree. The article you linked doesn’t mention how precise the estimations are, but I can’t imagine they’re that precise

Is it really hotter now than any time in 100,000 years?:

Without rapid and sustained reductions in greenhouse gas emissions, the Earth is currently on course to reach temperatures of roughly 3 C (5.4 F) above preindustrial levels by the end of the century, and possibly quite a bit higher.

At that point, we would need to look back millions of years to find a climate state with temperatures as hot. That would take us back to the previous geologic epoch, the Pliocene, when the Earth’s climate was a distant relative of the one that sustained the rise of agriculture and civilization.