At the gas venting rates observed in some seafloor localities, heat advection and the latent heat of hydrate crystallization could significantly warm the subsurface, reduce the hydrate stability zone thickness, and decompose previously crystallized hydrate. Effects of heat advection and the latent heat of hydrate crystallization are limited by the duration of time over which venting occurs and ultimately by the time it takes to plug vents with hydrate, however. We examine the connection between gas venting, hydrate crystallization, and subsurface temperature using a new one-dimensional analytical solution to the steady state heat flow equation with constant hydrate crystallization, and we examine the effects of the duration of venting employing one-dimensional finite element solutions to the transient heat flow equation that include space- and time-dependent hydrate dissolution and crystallization. We show that if lateral losses of heat are negligible, hydrate crystallization and the advection of heat by gas flow at the more vigorous rates of gas discharge observed on the seafloor could increase the temperature gradient near the surface by more than an order of magnitude and decrease the feed gas hydrate stability zone thickness from ~570 to <200 m before the vents plug with hydrate. We compute how the chemistry of the venting gas and crystallizing hydrate evolve as a vent plugs with hydrate.