I'm not even sure that I understand the question, but I'm pretty sure that I don't know the answer.
To my knowledge, some of the methane is from organic material that was forced into the Earth's crust in tectonic subduction zones. Other sources are less well-understood, and some believe that there are inorganic mechanisms for the production of hydrocarbons deep in the mantle. All very speculative stuff. Anyway, surface temperatures certainly affect organic deposits at the ocean floor, which can then be subducted. So a change in atmospheric temperature would alter the amount of methane being released after subduction, which would then affect atmospheric temperatures. Is that the kind of feedback that you mean? If so, I have no idea whether it's a positive or negative feedback loop, or what the significance might be anyway.