The way this works is, we run a computer model and try to come up with a scenario which matches the observations from that time period the best. And seems like the extreme warning that happened during the PETM was likely due to methane hydrate dissociation. I can link a few scientific papers if anyone is interested.
Edit : https://en.m.wikipedia.org/wiki/Paleocene–Eocene_Thermal_Max...
This is a good write-up. I'd still appreciate big picture commentary from domain experts, though.
This is my PhD adviser's paper. It is best to date estimate on the rate of carbon emissions during the PETM: https://www.soest.hawaii.edu/oceanography/faculty/zeebe_file...
It was really warm, not sure on the exact number off the top of my head but at least 10-15 degrees C warmer in high latitudes than today. It was essentially an ice free world. And during the PETM event itself, the temperatures rose another 5 to 8 degrees C: https://dspace.library.uu.nl/bitstream/handle/1874/385777/Ex...