To capture salient contextual information for spoken language understanding (SLU) of a dialogue, we propose time-aware models that automatically learn the latent time-decay function of the history without a manual time-decay function. We also propose a method to identify and label the current speaker to improve the SLU accuracy. In experiments on the benchmark dataset used in Dialog State Tracking Challenge 4, the proposed models achieved significantly higher F1 scores than the state-of-the-art contextual models. Finally, we analyze the effectiveness of the introduced models in detail. The analysis demonstrates that the proposed methods were effective to improve SLU accuracy individually.