Heat flow measurements across the Washington-Oregon convergent margin show several characteristic features: a well defined peak at the foot of the overthrust, a gradual decrease landward across the lower slope reaching a minumum at the ridge, and a gradual rise further landward. Constrained by geological and seismic evidence on the rate of stacking and the dimension of stacked thrust sheets and by drilling results on sediment properties, we use a two-dimensional time-dependent finite element procedure to model the stacking of overthrust slices on sediments and to calculate the thermal structure beneath the lower slope of the accretionary prism; the calculated heat flow profile is in good agreement with the measurements. Advective heat transfer due to stacking of overthrust sheets and topographic changes are shown to play a dominant role in controlling the surface heat flow and the thermal state of the accretionary prism. ¿ American Geophysical Union 1988