Our Planet has a natural ecosystem comprised of living organisms and methane hydrates in deep marine environments. This ecosystem was constructed in the present work to examine the influence that subtle temperature fluctuations could have on the dynamic stability of the hydrate deposits. The coupled mass and energy balance equations that describe the microbial bioreactions, their consumption by feather duster worms, and methane hydrate dissociation confirm that the bioreaction kinetics are dominated by endothermic methanogenic metabolism that stabilizes methane hydrates with a fragile tolerance to 0.001K temperature increases. The feather duster worms also stabilize the hydrates via their selective consumption of methanotrophs that could otherwise overtake the system by their exothermic metabolism. Critical ocean temperature limits exist, beyond which hydrate dissociations would cause underwater eruptions of methane into the sea. Historical ocean temperature records and gas hydrate inventory estimates combined with our model suggests that hydrate deposits as deep as 560-meters below sea level could already be at risk, whereas the methane hydrate stability zone will retreat deeper as ocean temperatures rise. Slowing its retreat could avoid the massive release of greenhouse gas.