Medium-range numerical weather prediction (NWP) is crucial to human activities. Reliable weather forecasts allow better resource management and are essential for disaster preparation. Modern NWP models provide accurate medium-range forecasts, but they require some of the largest computing facilities currently available. Convolutional Neural Networks (CNNs) are data-driven architectures preserving the spatial relationship of data with a low number of learnable parameters, thus having the potential to relieve this computational cost. As CNNs were originally tailored for Euclidean domains, current data-driven NWP approaches are based on planar projections of the sphere, which induces important deformations. This work proposes a data-driven medium-range NWP approach using a CNN able to perform convolutions natively on the sphere and integrating the temporal dimension. The effect of static and dynamic atmospheric features, as well as of the temporal discretization, is tested on the predictive skill using a wide range of metrics. Experimental results show that our method is able to emulate complex patterns of common atmospheric fields, and that our predictions are able to accurately reproduce the seasonal cycle. Our model outperforms the global and weekly climatologies and the persistence baselines up to 5 days. In addition, our model produces state-of-the-art temperature predictions for short forecast lead times.