Multiphase flows of a number of immiscible fluids are often encountered in both engineering practice and in environment. Due to the interactions of heat conduction, radiation and multiphase fluid flow, thermal modeling of such systems becomes a challenging task. The heat transfer processes with phase change become additionally influenced by a nonlinear nature of the thermal radiative transport. Therefore, in most of the research related to above mentioned processes, one aspect of phenomena is being neglected. Practical use of developed numerical model is limited due to very high computational cost when all aspects are being analysed jointly. Complexity of such systems, integrated with time step and grid resolution leads to very high values of deegress of freedom ($ > 10^5 $) and so far DL-ROMs have been appliead to the reduction of scalar PDEs with at most $10^4$ deegrees of freedom. Therefore, in this research, recently developed POD-DL-ROM and RB-ML-ROM methodology will be applied as follows: (i) Computational fluid dynamics - snapshot collection/data collection, (ii) Dimensionality reduction, (iii) Training DL-ROM model, (iv) Testing - online phase.