A study of the effects for the original hypothesis, based on a coupled climate–carbon cycle model assessed a 1000-fold (from <1 to 1000 ppmv) methane increase—within a single pulse, from methane hydrates (based on carbon amount estimates for the PETM, with ~2000 GtC), and concluded it would increase atmospheric temperatures by more than 6 °C within 80 years. Further, carbon stored in the land biosphere would decrease by less than 25%, suggesting a critical situation for ecosystems and farming, especially in the tropics.
Atsushi Obata; Kiyotaka Shibata (June 20, 2012). “Damage of Land Biosphere due to Intense Warming by 1000-Fold Rapid Increase in Atmospheric Methane: Estimation with a Climate–Carbon Cycle Model”. J. Climate. 25 (24): 8524–8541. Bibcode:2012JCli…25.8524O. doi:10.1175/JCLI-D-11-00533.1.
National Science Foundation: 22 degrees F (12’C) in 50 years found in ice core, 11,700 years ago
“Because gas hydrates globally sequester such a large amount of methane at depths that are shallow compared to those associated with conventional gas, even reputable publications sometimes posit that warming climate will lead to catastrophic breakdown of global gas hydrate deposits and the subsequent injection of the released methane into the atmosphere. Our review underscores the implausibility of such scenarios. The spatial distribution of climate-susceptible gas hydrates, the strong sinks that consume much of the methane released from gas hydrate breakdown before the gas reaches the atmosphere, and the thermodynamic barriers to runaway gas hydrate breakdown all argue against strong synergy between gas hydrates and the climate system. In fact, we estimate that seafloor emissions of hydrate-derived methane (most of which never reaches the atmosphere) is dwarfed by annual carbon dioxide emissions to the atmosphere from anthropogenic sources.”
This still leaves the question “What could cause abrupt warming that is not methane?”