Tehran research reactor (TRR) is a material test reactor (MTR) that uses U3O8–Al fuel plates. Fuel plates are usually used in research reactors due to their great thermal characteristics. The occurrence of various accidents in nuclear reactors has increased the efforts to develop accident tolerant fuels (ATF). For this reason, intermetallic compounds of uranium and silicon, have been introduced as candidates for ATF. In this study, the heat transfer and melting of fuel plates composed of U3O8–Al, UO2–Zr, and U3Si2–Al, in normal operation and hypothetical heat transfer impairment in the TRR have been studied. These compounds are chosen as candidates for probable replacement in the new design of the TRR. In this work, two-dimensional equations of heat transfer and enthalpy using the finite difference method have been solved and solid to liquid phase changes are discussed. According to the findings of this research, during a hypothetical heat transfer impairment, UO2–Zr fuel undergoes a phase change from solid to liquid after a longer period of time compared to the other two fuels. This delay is attributed to the relatively high melting point of UO2–Zr, which is notably higher than the melting points of the other two fuels. It has been shown that when the focus is on transferring heat from the fuel plate to the coolant, U3Si2–Al performs better than the other two types of fuel due to its higher thermal conductivity and relatively good melting behavior.