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 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 its nominal point, the offdesign ORC engine power output reduces by a lesser extent than that of the ICE. At an ICE part-load operation of 60% (by power), the optimised ORC engine with fluids such as R1233zd operates at 77% of its nominal capacity. ORC off-design performance maps are generated, predicting system performance and can be used by ORC system designers, manufacturers and plant operators to identify optimum performance under real operating conditions.