Accurately measuring the average temp of the entire planet is not without a margin of error even in the modern age of satellites. I've read about how they estimated past values using sparse data points, written anecdotes, and inferences.
You guys just throw up graphs like it's gospel, applying zero healthy skepticism.
There is a science to using natural phenomenon as proxies. Sparse data points? Sure, as you go back in time it gets sparser. The published articles include error bars. The mercury thermometer was invented back in 1714, and by the middle of the 19th century, methodical records were being kept. Science didn't begin with the Manhattan Project.
You include "inferences" as if that's some kind of defect. What science doesn't use inference?