Solidification and cooling of a (con)casting, with the simultaneous heating of the mold, is a case of transient spatial heat and mass transfer. This paper introduces an original and universal numerical model of solidification, cooling and heating, of a one-to-three-dimensional stationary and transient temperature field in a system comprising the casting, the mold and its surroundings. This model simulates both traditional as well as non-traditional technologies of casting conducted in foundries, metallurgical plants, forging operations, heat-treatment processes, etc. The casting process is influenced not only by the thermophysical properties (i.e. heat conductivity, the specific heat capacity and density in the solid and liquid states) of the metallic and non-metallic materials, but also by the precision with which the numerical simulation is conducted. Determining these properties is often more demanding than the actual calculation of the temperature field of the solidifying object. Since the influence of individual properties should be neither under- nor over-estimated, it is necessary to investigate them via a parametric study. It is also necessary to determine the order of these properties in terms of their importance.