The use of organic Rankine cycle systems for waste heat recovery on heavy-duty vehicles is one of the most effective solutions to reduce the fuel consumption and the environmental pollution of heavy-duty transport. In this application, the variable driving conditions cause such systems to be operated with a highly fluctuating heat source, which must be primarily handled by properly designing the system components and, in particular, the evaporator. This paper investigates the effect of the design parameters of a fin-and-tube evaporator on the dynamic response of the organic Rankine cycle system. The goal is to understand and quantify the dampening effect given by the evaporator design parameters, which influence its weight, and, in turn, its dynamic time response. A finite-volume dynamic model of the evaporator is built in Dymola. Subsequently, the dynamic behaviour of the high-pressure part of the organic Rankine cycle system is simulated based on measurement data of the exhaust gas mass flow rate and temperature from a heavy-duty vehicle taken during a 45-min driving cycle. Simulations are carried out in MATLAB®/Simulink®, by importing the Dymola model as a functional mock-up unit. The results suggest that the larger the heat source fluctuations, the stronger the need to increase the evaporator weight to obtain appreciable dampening effects. The simultaneous variation of the inner diameter of the evaporator tube and the tube spacing leads to the highest dampening effect on the net power output, with a reduction of about 11% of the highest peak value (8220 W).