Recent years have witnessed interest in Temporal Question Answering over Knowledge Graphs (TKGQA), resulting in the development of multiple methods. However, these are highly engineered, thereby limiting their generalizability, and they do not automatically discover relevant parts of the KG during multi-hop reasoning. Relational graph convolutional networks (RGCN) provide an opportunity to address both of these challenges – we explore this direction in the paper. Specifically, we propose a novel, intuitive and interpretable scheme to modulate the messages passed through a KG edge during convolution based on the relevance of its associated period to the question. We also introduce a gating device to predict if the answer to a complex temporal question is likely to be a KG entity or time and use this prediction to guide our scoring mechanism. We evaluate the resulting system, which we call TwiRGCN, on a recent challenging dataset for multi-hop complex temporal QA called TimeQuestions. We show that TwiRGCN significantly outperforms state-of-the-art models on this dataset across diverse question types. Interestingly, TwiRGCN improves accuracy by 9–10 percentage points for the most difficult ordinal and implicit question types.