The supercritical Organic Rankine Cycle (ORC) for the Waste Heat Recovery (WHR) from Internal Combustion (IC) engines has been a growing research area in recent years, driven by the aim to enhance the thermal efficiency of the ORC and engine. Simulation of a supercritical ORC-WHR system before a real-time application is important as high pressure in the system may lead to concerns about safety and availability of components. In the ORC-WHR system, the evaporator is the main contributor to thermal inertia of the system and is considered to be the critical component since the heat transfer of this device influences the efficiency of the system. Since the thermo-physical properties of the fluid at supercritical pressures are dependent on temperature, it is necessary to consider the variations in properties of the working fluid. The well-known Finite Volume (FV) discretization method is generally used to take those property changes into account. However, a FV model of the evaporator in steady state condition cannot be used to predict the thermal inertia of the cycle when it is subjected to transient heat sources. In this paper, a dynamic FV model of the evaporator has been developed and integrated with other components in the ORC-WHR system. The stability and transient responses along with the performance of the ORC-WHR system for the transient heat source are investigated and are also included in this paper.