Hundreds of plumes of methane bubbles, first observed in 2008, emanate from an area of the seabed off West Svalbard that has become 1°C warmer over the past 30 years. The distribution of the plumes, lying close to and upslope from the present upper limit of the methane hydrate stability zone, indicates that methane in the plumes could come from warming-induced hydrate dissociation, a process commonly invoked as contributing to rapid climate change. We used numerical modeling to investigate the response of hydrate beneath the seabed to changes in bottom-water temperature over periods of up to 1000 years B.P. The delay between the onset of warming and emission of gas, resulting from the time taken for thermal diffusion, hydrate dissociation, and gas migration, can be less than 30 years in water depths shallower than the present upper limit of the methane hydrate stability zone, where hydrate was initially several meters beneath the seabed and fractures increase the effective permeability of intrinsically low-permeability glacigenic sediment. At the rates of warming of the seabed that have occurred over the past two centuries, the enthalpy of hydrate dissociation limits the rate of gas release to moderate values. Cycles of warming and cooling can create and sustain hydrate close to the seabed where there is locally a supply of methane of tens of mol·m–2 yr–1. This rate of gas flow can be achieved where stratigraphic and structural heterogeneity focus gas migration, although the regional rate of methane supply could be much less.