Carbon recycling by CO₂ mineralization is one of technical options to break dependence on fossil fuels for the iron and steel making industry. We previously introduced "super-slow" cooling of molten slags as a method to increase the CO₂ mineralization rate of slag to make carbon recycling feasible. To design the operating conditions, the solidification process and temperature history of molten slag with complex compositions should be simulated. This study builds and validates a solidification heat transfer model using literature-reported experimental data of the time-dependent temperature distributions of blast furnace slag ambiently cooled in a shallow-plate container. One dimensional vertical heat transfer was modelled considering conduction, natural convection, radiation, the latent heat of solidification, and nucleation timing. The time-temperature-transformation diagram and thermophysical properties of the slag was estimated using our in-house deep neural network trained on literature data. Temperature histories at three distinct points in the slag closely matched measured temperatures and all crystalline states were consistent with the experimental results, which means the temperature histories with solidification can be predicted by phenomenalistic approach to thermophysical properties including latent heats. In future work, the validated simulation code will be applied to basic oxygen furnace slag to design the super-slow cooling operation.