Lots of different independent methods and sources that correlate, along with some approximations. Actual measured readings aren't as accurate or match up in the early periods, which is why the IPCC decided to use 1980 as a baseline to start from for consistent and abundant data to compare with. This continues to be a side argument about if we're really past 1.5C or not, since the graphs start differently. The "good" news is that as time goes on, that argument becomes less relevant because the differences shrink and catastrophic converges.