Answering natural language questions with temporal intent on knowledge graphs (TKGQA) has attracted rising attention in recent years. TKGQA contains several subtasks, such as implicit expression parsing, relevant facts searching, and subgraph logic reasoning, and they are composed in a pipelined manner to finish the final task. Previous work learns isolated models for each subtask, which severely restricts the knowledge sharing between related subtasks and settings, leading to underperformance. Recently, Large Language Models (LLMs) have unlocked strong multi-task capabilities from reading instructive prompts. Motivated by these, we propose a unified generation framework based on instruction tuning, called InstructTQA, for TKGQA, which unifies the key subtasks in TKGQA via text generation. Besides, to improve the time-sensitivity of LLMs, we also design several auxiliary subtasks. By capturing inter-task dependency and collaboratively learning general knowledge from different subtasks, InstructTQA demonstrates superior performance compared to the state-of-the-art one on the MultiTQ dataset, thereby substantiating its efficacy in addressing the TKGQA task.