The heat flow data are important in many aspects including interpretation of various geophysical observations, solutions of important engineering problems, modelling of the ice dynamics, and related environmental assessment. However, the distribution of the direct measurements is quite heterogeneous over the Earth. Different methods have been developed during past decades to create continuous maps of the geothermal heat flow (GHF). Most of them are based on the principle of similarity of GHF values for the lithosphere with comparable age and tectonic history or inversion of magnetic field data. Probabilistic approach was also used to realize this principle. In this paper, we present a new method for extrapolating the GHF data, based on the inversion of a geophysical data set using optimization problem solution. We use the results of inversion of seismic and magnetic field data into temperature and data from direct heat flow measurements. We use the Arctic as the test area because it includes the lithosphere of different ages, types, and tectonic settings. In result, the knowledge of GHF is important here for various environmental problems. The resulting GHF map obtained well fits to the observed data and clearly reflects the lithospheric domains with different tectonic history and age. The new GHF map constructed in this paper reveals some significant features that were not identified earlier. In particular, these are the increased GHF zones in the Bering Strait, the Chukchi Sea and the residual GHF anomaly in the area of the Mid-Labrador Ridge. The latter was active during the Paleogene.