The relevance of the study is related to the determination of the thermal characteristics of the IVG.1M research reactor core with the low enriched uranium fuel under the nominal and design operating modes. The thermal technological condition of the IVG.1M research reactor during the start-up are determined by the readings of the temperature, pressure and coolant flow sensors of the information and measuring system. The indirect methods including the computer simulating ones are used to determine the temperature of the core structural materials and the distribution of the coolant temperature by the height of the fuel assembly. The research has been carried out using the method of the finite element analysis using the ANSYS Fluent software package. The study goal was to verify the adequacy of the calculation methodology and obtain the calculated data on the temperature distribution in the fuel assembly in the reactor power range from the nominal to design one. The article presents a description of the IVG.1M reactor, the research methodology, computer model, simulation results and the comparison of the calculated data with the experimental ones. The study scientific novelty consists in determining the temperature conditions of the fuel rods during the reactor operation at various levels of the design capacity with a conservative approach to the cooling conditions. The significance of the research results lies in the fact that a computer model can be used to determine the characteristics of the IVG.1M reactor core under the reactor various operating modes and to analyze the thermohydraulic processes in the fuel assembly.