Rheumatic heart disease (RHD) affects an estimated 39 million people worldwide and is the most common acquired heart disease in children and young adults. Echocardiograms are the gold standard for diagnosis of RHD, but there is a shortage of skilled experts to allow widespread screenings for early detection and prevention of the disease progress. We propose an automated RHD diagnosis system that can help bridge this gap. Experiments were conducted on a dataset with 11646 echocardiography videos from 912 exams, obtained during screenings in underdeveloped areas of Brazil and Uganda. We address the challenges of RHD identification with a 3D convolutional neural network (C3D), comparing its performance with a 2D convolutional neural network (VGG16) that is commonly used in the echocardiogram literature. We also propose a supervised aggregation technique to combine video predictions into a single exam diagnosis. The proposed approach obtained an accuracy of 72.77% for exam diagnosis. The results for the C3D were significantly better than the ones obtained by the VGG16 network for videos, showing the importance of considering the temporal information during the diagnostic. The proposed aggregation model showed significantly better accuracy than the majority voting strategy and also appears to be capable of capturing underlying biases in the neural network output distribution, balancing them for a more correct diagnosis. Automatic diagnosis of echo-detected RHD is feasible and, with further research, has the potential to reduce the workload of experts, enabling the implementation of more widespread screening programs worldwide.