In this study, a hybridized neuro-genetic optimization methodology realized by embedding finite element analysis (FEA) trained artificial neural networks (ANN) into genetic algorithms (GA), is used to optimize temperature control in a ceramic based continuous flow polymerase chain reaction (CPCR) device. The CPCR device requires three thermally isolated reaction zones of 94 degrees C, 65 degrees C, and 72 degrees C for the denaturing, annealing, and extension processes, respectively, to complete a cycle of polymerase chain reaction. The most important aspect of temperature control in the CPCR is to maintain temperature distribution at each reaction zone with a precision of +/-1 degree C or better, irrespective of changing ambient conditions. Results obtained from the FEA simulation shows good comparison with published experimental work for the temperature control in each reaction zone of the microfluidic channels. The simulation data are then used to train the ANN to predict the temperature distribution of the microfluidic channel for various heater input power and fluid flow rate. Once trained, the ANN analysis is able to predict the temperature distribution in the microchannel in less than 20 min, whereas the FEA simulation takes approximately 7 h to do so. The final optimization of temperature control in the CPCR device is achieved by embedding the trained ANN results as a fitness function into GA. Finally, the GA optimized results are used to build a new FEA model for numerical simulation analysis. The simulation results for the neuro-genetic optimized CPCR model and the initial CPCR model are then compared. The neuro-genetic optimized model shows a significant improvement from the initial model, establishing the optimization method's superiority.