We propose a context-aware neural network model for temporal information extraction, with a uniform architecture for event-event, event-timex and timex-timex pairs. A Global Context Layer (GCL), inspired by the Neural Turing Machine (NTM), stores processed temporal relations in the narrative order, and retrieves them for use when the relevant entities are encountered. Relations are then classified in this larger context. The GCL model uses long-term memory and attention mechanisms to resolve long-distance dependencies that regular RNNs cannot recognize. GCL does not use postprocessing to resolve timegraph conflicts, outperforming previous approaches that do so. To our knowledge, GCL is also the first model to use an NTM-like architecture to incorporate the information about global context into discourse-scale processing of natural text.