A combination of a fuzzy inference system (FIS) and a differential evolution (DE) algorithm, known as the differential evolution-based fuzzy inference system (DEFIS), is developed for the prediction of natural heat transfer in Cu–water nanofluid within a cavity. In the development of the hybrid model, the DE algorithm is used for the training process of FIS. For this purpose, first, the case study is simulated using the computational fluid dynamic (CFD) method. The CFD outputs, including velocity in the y-direction, the temperature of the nanofluid, and the nanoparticle content (Ø), are employed for the learning process of the DEFIS model. By choosing the optimum number of inputs and the number of population, the underlying DEFIS variable parameters are studied. After reaching the high value of DEFIS intelligence, in the learning step, a variety of Ø values (e.g., 0.5, 1, and 2) are reviewed. For the full intelligence of DEFIS, the velocity of the nanofluid is predicted in further nodes of the cavity domain. Finally, the velocity of the nanofluid is predicted by using the data at Ø = 0.15, which are absent in the DEFIS process.