To drive an atmospheric general circulation model, sea surface temperatures (SSTs) are needed as lower boundary condition. These are well known for the modern ocean, but for other time slices the database is very sparse, and often complete global SST fields are not available. To circumvent this problem, the SIMPLE ocean model has been developed, which estimates surface currents in a diagnostic manner from surface winds. Horizontal heat transports by advection and diffusion and surface heat fluxes are used to calculated SSTs. The unknown transports from the deep ocean are inversely estimated from sparse SST data. The model can be understood as a method to estimate a global SST field from a sparse data set, where it takes into account the wind driven surface circulation. The SIMPLE model is applied to a set of Last Glacial Maximum SSTs reconstructed from a new South Atlantic core data set. The resultant completed SST field exhibits more structure than the CLIMAP reconstruction with larger glacial cooling in the central equatorial Atlantic and off the shore of Angola/Namibia and less cooling in the central South Atlantic.