We propose a deep learning-based method that uses spatial and temporal information extracted from the sub-6GHz band to predict/track beams in the millimeter-wave (mmWave) band. In more detail, we consider a dual-band communication system operating in both the sub-6GHz and mmWave bands. The objective is to maximize the achievable mutual information in the mmWave band with a hybrid analog/digital architecture where analog precoders (RF precoders) are taken from a finite codebook. Finding a RF precoder using conventional search methods incurs large signalling overhead, and the signalling scales with the number of RF chains and the resolution of the phase shifters. To overcome the issue of large signalling overhead in the mmWave band, the proposed method exploits the spatiotemporal correlation between sub-6GHz and mmWave bands, and it predicts/tracks the RF precoders in the mmWave band from sub-6GHz channel measurements. The proposed method provides a smaller candidate set so that performing a search over that set significantly reduces the signalling overhead compared with conventional search heuristics. Simulations show that the proposed method can provide reasonable achievable rates while significantly reducing the signalling overhead.