But this fails to answer the critical question - was the release the cause of the warming? Or an effect of the warming?
In the case of the PETM, the release was, with near certainty, the cause of the warming. The PETM is a very interesting climate "incident" -- I've never been able to find a discussion of what triggered the release. But the temperature increase clearly lags the increasing carbon dioxide and methane concentrations in the atmosphere.
I can find links for you, or you can Google for them yourself. Goddard Institute of Space Studies had an article about "ocean burps" that I've posted here a few times.