This paper identifies and describes the parameters of a numerical model generating the microstructure in the integrated heating-remelting-cooling process of steel specimens. The numerical model allows the heating-remelting-cooling process to be simulated comprehensively. The model is based on the Monte Carlo (MC) method and the finite element method (FEM), and works within the entire volume of the steel sample, contrary to previous studies, in which calculations were carried out for selected, relatively small areas. Experimental studies constituting the basis for the identification and description of model parameters such as: probability function, initial number of orientations, number of cells and number of MC steps were carried out using the Gleeble 3800 thermo-mechanical simulator. The use of GPU capabilities improved the performance of the numerical model and significantly reduced the simulation time. Thanks to the significant acceleration of simulation times, it became possible to comprehensively implement a numerical model of the heating-transformation-cooling process in the entire volume of the test sample. The paper is supplemented by results of performance tests of the numerical model and results of simulation tests.