The cooling of the oceanic lithosphere causes subsidence by isostasy. This subsidence results in the formation of ocean basins. In this paper we assume that the subsiding lithosphere is covered with sediments. A similarity solution is obtained for the coupled problem of heat conduction in the sediments and basement. The subsidence history of the sedimentary basin is obtained from isostasy. For reasonable values of parameters the heat conduction in the sediments does not affect the subsidence, which is proportional to t1/2. It is also a good approximation to assume a linear temperature profile in the sediments with a slope proportional to t-1/2.