Organic Rankine cycle (ORC) engines often operate under variable heat-source conditions, so maximising performance at both nominal and off-design operation is crucial for the wider adoption of this technology. In this work, an off-design optimisation tool is developed and used to predict the impact of varying heat-source conditions on ORC operation. Unlike previous efforts where the performance of ORC engine components is assumed fixed, here we consider explicitly the time-varying operational characteristics of these components. A bottoming ORC system is first optimised for maximum power output when recovering heat from the exhaust gases of an internal-combustion engine (ICE) running at full load. A double-pipe heat exchanger (HEX) model is used for sizing the ORC evaporator and condenser, and a piston-expander model for sizing the expander. The ICE is then run at part-load, thus varying the temperature and mass flow rate of the exhaust gases. The tool predicts the new off-design heat transfer coefficients in the heat exchangers, and the new optimum expander operating points. Results reveal that the ORC engine power output is underestimated by up to 17% when the off-design operational characteristics of these components are not considered. In particular, the piston-expander isentropic efficiency increases at off-design operation by 10–16%, due to the reduced pressure ratio and flow rate in the system, while the evaporator effectiveness improves by up to 15%, due to the higher temperature difference across the HEX and a higher proportion of heat transfer taking place in the two-phase evaporating zone. As the ICE operates further away from its nominal point, the off-design ORC engine power output reduces by a lesser extent than that of the ICE. At an ICE part-load operation of 60% (by electrical power), the optimised ORC engine with fluids such as R1233zd operates at 77% of its nominal capacity. ORC off-design performance maps are generated, for characterising and predicting system performance, which can be used, along with the optimisation tool, by ORC system designers, manufacturers and plant operators to identify optimum performance under real operating conditions.