Continuous casting comprises thermal, mechanical and chemical processes running in a complex system that contains a number of elements, such as a solidifying steel strand, a mould with an oscillation mechanism, a withdrawal mechanism, a water cooling subsystem with nozzles, several control subsystems , etc. An external observer might see the process as robust and stable, but in reality there are fluctuations in the internal thermal and mechanical quantities, reflected in the structure and quality of the product. The research on unsteady behaviour of the quantities such as a solidifying strand temperature field, solid shell thickness and metallurgical length was conducted using an industrial diagnostic system DGS complemented with special measurement equipment and a thermal numerical model. Selected results of the monitoring and simulation of the non-standard process states are shown and analysed in the paper. Methods for determining the boundary conditions for the numerical model are also presented. The effect of the Leidenfrost phenomenon on the heat-transfer coefficient during water cooling by nozzles is also discussed. Since the determination of precise and immediate boundary conditions has technical limits, the model provides only smoothed values in time and space. As knowledge of the instantaneous state of the fluctuating process is a prerequisite for achieving quality and defect-free production, it is appropriate to complement the thermal numerical model by on-line monitoring of the machine's internal state. The results of the simulations are closely linked to the real process data.