Purpose – To develop the mathematical model, which allows predicting the temperature and flow distribution of an opaque glass melt with the temperature-dependent properties in case it is generated by electromagnetic and thermal convection. Analysis has been done for geometry of the model crucible with the immersed rod electrodes. Numerical analysis is used as a tool for finding out the parameters of the system, which allow getting desiderated homogeneity of temperature field by EM action. Design/methodology/approach – ANSYS CFX software is implemented for coupling of EM, thermal and HD processes in the modelled system. Usability of non-inductive approximation is shown using a full harmonic analysis in ANSYS. Findings – External magnetic field can impact the temperature distribution in the whole volume of the melt significantly, it relocates the hottest zones and changes the maximal temperature in the melt. Qualitative agreement between the numerical and experimental results has been obtained. Dependence of the potential difference between the electrodes on the velocity and temperature range has been examined. Impact of different thermal boundary conditions has been analysed. Research limitations/implications – Effects analysed in the publication occur in each conducting media subjected to the impact of simultaneous electrical and magnetical field. The main limitation is non-transparency of the melt. Practical implications – The purpose is to develop a mathematical tool for parameter optimisation of real glass melting furnace. Originality/value – In the present model temperature dependent properties of the melt have been taken into account, which has been neglected in previous models.