Offshore permafrost plays a role in the global climate system, but observations of permafrost thickness, state, and composition are limited to specific regions. The current global permafrost map shows potential offshore permafrost distribution based on bathymetry and global sea level rise. As a first‐order estimate, we employ a heat transfer model to calculate the subsurface temperature field. Our model uses dynamic upper boundary conditions that synthesize Earth System Model air temperature, ice mass distribution and thickness, and global sea level reconstruction and applies globally distributed geothermal heat flux as a lower boundary condition. Sea level reconstruction accounts for differences between marine and terrestrial sedimentation history. Sediment composition and pore water salinity are integrated in the model. Model runs for 450 ka for cross‐shelf transects were used to initialize the model for circumarctic modeling for the past 50 ka. Preindustrial submarine permafrost (i.e., cryotic sediment), modeled at 12.5‐km spatial resolution, lies beneath almost 2.5 ×10⁶km² of the Arctic shelf. Our simple modeling approach results in estimates of distribution of cryotic sediment that are similar to the current global map and recent seismically delineated permafrost distributions for the Beaufort and Kara seas, suggesting that sea level is a first‐order determinant for submarine permafrost distribution. Ice content and sediment thermal conductivity are also important for determining rates of permafrost thickness change. The model provides a consistent circumarctic approach to map submarine permafrost and to estimate the dynamics of permafrost in the past.