A huge amount of extra CO~2~ showed up. We don't have a definitive answer as to where from.

The cause is uncertain for now.

It's known with certainty that polar ice did not exist then - so it was not Antarctic melting giving a feedback bump. Besides the feedback bump caused by Antarctic melting is speculated to be on the order of 2 degrees.

It could have been partly volcanic, but not mainly volcanic. It certainly wasn't tectonic, as the event was a brief spike of "only" ~200 000 years.

The study below, somewhat speculative in nature, proposes that bottom water warming occurred 3000 years before the carbon trip, and decomposition of methane hydrates could have been the amplifier of the process. Which, to me, suggests that maybe the cause was geological.

https://pubmed.ncbi.nlm.nih.gov/18097406/

A hypothesis referenced in Wikipedia: a lot of high-carbon rock (kimberlite) experienced a volcanic eruption that released much CO2, and brought oceans above the theshold where methane hydrates decomposed and supplied methane.

Although the cause of the initial warming has been attributed to a massive injection of carbon (CO2 and/or CH4) into the atmosphere, the source of the carbon has yet to be found. The emplacement of a large cluster of kimberlite pipes at ~56 Ma in the Lac de Gras region of northern Canada may have provided the carbon that triggered early warming in the form of exsolved magmatic CO2. Calculations indicate that the estimated 900–1,100 Pg[194] of carbon required for the initial approximately 3 °C of ocean water warming associated with the Paleocene-Eocene thermal maximum could have been released during the emplacement of a large kimberlite cluster.[195] The transfer of warm surface ocean water to intermediate depths led to thermal dissociation of seafloor methane hydrates, providing the isotopically depleted carbon that produced the carbon isotopic excursion. The coeval ages of two other kimberlite clusters in the Lac de Gras field and two other early Cenozoic hyperthermals indicate that CO2 degassing during kimberlite emplacement is a plausible source of the CO2 responsible for these sudden global warming events.