This paper introduces TEMPLE-MQA, a novel framework for multi-hop question answering (MQA) under temporal knowledge editing. The framework addresses the challenge of handling questions with explicit temporal contexts, which previous methods struggle with due to their reliance on dense retrieval that lacks temporal awareness. TEMPLE-MQA constructs a time-aware graph (TAG) to store edit knowledge in a structured format, enabling effective temporal context preservation. It then employs an inference path, structural retrieval, and joint reasoning to derive answers. The framework outperforms existing methods on benchmark datasets, including the newly proposed TKEMQA dataset, which is the first benchmark tailored for MQA with temporal scopes. TEMPLE-MQA also introduces a novel planning procedure and joint reasoning approach for the inference path, along with a unique structural retrieval method for knowledge retrieval. The framework is applicable to a broader range of scenarios, including the processing of temporal information. The experiments demonstrate that TEMPLE-MQA significantly improves performance on MQA tasks under temporal knowledge editing, particularly in scenarios involving multiple reasoning steps and temporal constraints. The results show that TEMPLE-MQA achieves higher accuracy and stability compared to existing methods, especially when dealing with large-scale edits. The framework's ability to distinguish between historical and updated knowledge makes it particularly effective in temporal contexts.This paper introduces TEMPLE-MQA, a novel framework for multi-hop question answering (MQA) under temporal knowledge editing. The framework addresses the challenge of handling questions with explicit temporal contexts, which previous methods struggle with due to their reliance on dense retrieval that lacks temporal awareness. TEMPLE-MQA constructs a time-aware graph (TAG) to store edit knowledge in a structured format, enabling effective temporal context preservation. It then employs an inference path, structural retrieval, and joint reasoning to derive answers. The framework outperforms existing methods on benchmark datasets, including the newly proposed TKEMQA dataset, which is the first benchmark tailored for MQA with temporal scopes. TEMPLE-MQA also introduces a novel planning procedure and joint reasoning approach for the inference path, along with a unique structural retrieval method for knowledge retrieval. The framework is applicable to a broader range of scenarios, including the processing of temporal information. The experiments demonstrate that TEMPLE-MQA significantly improves performance on MQA tasks under temporal knowledge editing, particularly in scenarios involving multiple reasoning steps and temporal constraints. The results show that TEMPLE-MQA achieves higher accuracy and stability compared to existing methods, especially when dealing with large-scale edits. The framework's ability to distinguish between historical and updated knowledge makes it particularly effective in temporal contexts.