This paper presents a novel nonlinear dictionary learning (DL) model to address the energy disaggregation (ED) problem, i.e., decomposing the electricity signal of a home to its operating devices. First, ED is modeled as a new temporal DL problem where a set of dictionary atoms is learned to capture the most representative temporal features of electricity signals. The sparse codes corresponding to these atoms show the contribution of each device in the total electricity consumption. To learn powerful atoms, a novel deep temporal DL (DTDL) model is proposed that computes complex nonlinear dictionaries in the latent space of a long short-term memory autoencoder (LSTM-AE). While the LSTM-AE captures the deep temporal manifold of electricity signals, the DTDL model finds the most representative atoms inside this manifold. To simultaneously optimize the dictionary and the deep temporal manifold, a new optimization algorithm is proposed that alternates between finding the optimal LSTM-AE and the optimal dictionary. To the best of authors' knowledge, DTDL is the only DL model that understands the deep temporal structures of the data. Experiments on the Reference ED Data Set show an outstanding performance compared with the recent state-of-the-art algorithms in terms of precision, recall, accuracy, and F-score.