The path which subducting lithosphere follows can be broken into three zones: zone I, a subhorizontal region of nearly constant dip near the trench; zone II, a region of rapidly increasing dip; and zone III, a region generally deeper than 125 km, again of nearly constant dip. We have modeled the thermal evolution of slabs as they pass through these three zones using the method of lines, a numerical technique well suited to the solution of time dependent partial differential equations. By use of appropriate initial conditions and time dependent boundary conditions we can simulate subduction with variations in age of subducting lithosphere, slab velocities, and paths followed by the slab. Thermal modeling results indicate that the geometry of the slab in region II can be empirically related directly to the thermal structure of the slab in that region and thus indirectly to age and velocity. It follows that low angle subduction can extend several hundred kilometers inland only in cases of high convergent velocities (>15 cm yr-1) and old (>120 m.y.) lithosphere. We further suggest that rapid variations in the convergence velocities can provide an enabling mechanism for back arc spreading while slow changes in convergence velocities and/or age variations in the subducting lithosphere lead to migration of volcanic arcs.