The ratio of 16O to 18O in water gives an indication of ocean temperature (water with Oxygen atomic weight of 16 evaporates a bit faster than water with Oxygen atomic weight of 18).
The kinds of pollen found in lake sediments also gives an indication of nearby temperatures, the presence of dryas pollen is an indication of a centuries long cold snap, e.g. Younger Dryas.
Historical records give an indication of climate. One example is the records of the dates of charry blossoms in Japan going back moe than 1300 years. Another example is the Viking settlements in Greenland, there were working farms on land that is now permafrost.
Another method is temperature logging of boreholes, one major problem with the technique is that time resolution gets worse the farther back in time.
Another is looking at the locations of tree lines.