Rail vehicles are developed towards higher speed and higher axle load, requiring robust mechanical brake systems for running safety. One of the most important mechanical brake systems is the disc brake, which converts the kinetic energy of rail vehicles into heat. A high brake disc temperature reduces the coefficient of friction between the brake disc and the brake pad, and causes high thermal stress, which, in turn, induces thermal cracks on the brake disc. To avoid these negative impacts, it is necessary to understand how friction heat is generated and dissipated. Experimental investigation is relatively complex, so numerical studies are an effective method to address this issue. The objective of this research is to model the temperature development of a rail vehicle brake disc during braking, which involves contact mechanics, heat transfer and fluid mechanics. Most studies use simple analytical solutions or complex commercial Finite Element Method (FEM) software to calculate the temperature of the brake disc, which lacks accuracy or is computationally heavy, respectively. Hence, we aim to develop a new FEM model, which is accurate and fast to solve. The methodology includes deriving the partial differential equations of the brake-related phenomena, including contact mechanics, heat transfer and fluid mechanics. Heat is generated through friction rather than applied heat flux on the contact surface. Heat conduction, convection, and radiation are considered. The airflow around the brake is considered to get the heat convection coefficient. Then, the basis functions are chosen and the mass and stiffness matrices, and the load vector are assembled. However, we still need powerful computer to accelerate our simulation, so we need the help of NAISS. More advanced research can be conducted based on this FEM model, including sensitivity analysis of railway brake disc temperature development and an adaptive mesh to reduce the computation time.