The unconventional natural gas resource program of the Department of Energy has targeted ancient subduction zones as a possible source of organic-origin natural gas. The suggestion is that organic sediments which have been accreted in the prism and/or subducted beneath the prism will produce gas at greater depths than in more conventional, generally hotter, basins. A critical element in determining the likelihood of gas generation in ancient or modern accretionary prisms is the thermal regime of the accreting prism. We have developed a computer model to determine the overall thermal regime in the modern forearcs of Oregon/Washington and southern Alaska. This allows us to predict the likelihood that gas has been generated at depth in the forearc prism, or within sediments as they are subducted beneath the prism. In fact, the model results indicate that subduction and accretion of these sediments at low temperatures increases the probability that ancient subduction zones, once accreted to the craton and allowed to heat in response to migration of the volcanic front, could be the source of natural gas. 75 refs., 24 figs.