In this article, a reduced numerical model for the heat transfer in a commonly used Thermit rail welding procedure is presented. A geometrically reduced calculation domain was deduced from the welding system consisting of rails, weld material and mold. The geometrical domain is restricted to heat transfer in the rail web. Unsteady heat conduction in base rail and weld regions undergoing melting and solidification are modeled using the finite difference method. Therefor the consecutive periods of the process are described by specified initial and boundary conditions: preheating, tapping time, pouring and the final cooling. The solid-liquid phase change occurring during pouring and cooling is described using the enthalpy method. Thermal radiation between rail and mold surfaces is considered. Validation is carried out against results of models using computational fluid dynamics and solidus temperature isothermal positions in micrographs of longitudinal weld cuts from experiments. A sensitivity analysis was performed for the reduced model. The temperature of the liquid steel melt and the specific heat of the rail steel have the largest impact on the fusion zone width whereas mold material properties show negligible influences. The calculated width of the final fusion zone agrees within a deviation of 16% to experimental results.