This work proposes modifications to the adaptive update law for a cerebellar model articulation controller (CMAC) and develops a model of a transcritical organic rankine cycle (ORC) to test it on. Owing to the local nature of its basis functions, the CMAC exhibits more weight drift (overlearning) than other types of neural networks, and practical applications have been restricted to systems without persistent oscillations of the inputs. The proposed solution to this problem here involves identifying a set of weights that is the best found so far in the training, and keeps the weights from drifting too far from these best weights. The method results in uniformly ultimately bounded signals, established through Lyapunov analysis. To show the improved training algorithm now allows the CMAC to control more general systems, it is applied to the control of a transcritical ORC. Part of the contribution of this paper also includes developing a model to describe the behaviour of a supercritical fluid in the ORC evaporator. The control method is compared with proportional–integral control, where the controls have to provide robustness to fluctuations and step changes in heat source temperatures.