Cooling, with the subsidence of continental crust, is likely to be an important mechanism for the formation of sedimentary basins. If the lithosphere was initially very thin and sedimentation continued to fill the basin to the original depth of basement, a similarity solution is possible. In this paper the similarity solution is extended to include sediment compaction and a depth-dependent thermal conductivity. The similarity solution is also used to determine the thermal evolution and petroleum potential of sedimentary basins. Experience with similarity solutions in many branches of applied physics indicates that they commonly give good results even when the required assumptions are rather poor approximations. An empirical subsidence relation valid for older basins is al o extended to include sediment compaction. These results are applied to the evolution of the Baltimore Canyon Trough on the outer continental margin of the eastern United States as given by the COST B-2 well. Good agreement is obtained with both the subsidence record and the present thermal gradient. It is predicted that optimal thermal conditions for the conversion of kerogens to petroleum occur between depths of 4 and 6 km.