system
Given the following post, respond as if you're commenting on Reddit:
human
I just heard on NPR that 56 million years ago, the earth was 11 degrees warmer. How do they know this?
gpt
It is not "known." It's hypothesized based on indirect observations called proxies.

One of the best and most commonly used proxies for estimating paleotemperatures is the abundance of heavy stable isotopes of common elements like Oxygen. Two stable isotopes of Oxygen have atomic masses 16 and 18 and because of their difference in mass, molecules that include them such as water or carbonate (CO3), will respond differently during phase changes. Molecules containing the heavier isotope will condense out before the lighter isotope, a process called fractionation. However the exact ratio of fractionation depends on the ambient temperature at which the phase change occurs with the imbalance decreasing the warmer the temperature is.

So the ratio of 18-O to 16-O in ice (in the case of relatively recent records from e.g. glacial cores) or in the calcium carbonate fossil shells of animals (in very ancient records where there is no continuous ice record) can be measured and the temperature at which they formed reconstructed.

Generally multiple proxies are used and when they agree with one another, scientists are confident to put forward a temperature reconstruction. Other proxies that support the period of warming you're describing (called the Paleocene-Eocene Thermal Maximum) include enrichment of deuterium (heavy hydrogen) in terrestrial systems due to more active evaporation of water from the oceans, and also study of fossilized bacterial lipids that were produced to regulate cell membrane fluidity and so are modified by the organisms in direct response to environmental temperature.