Temporal Knowledge Graph Question Answering (TKGQA) demands multi-hop reasoning under temporal constraints. Prior approaches based on large language models (LLMs) typically rely on rigid, hand-crafted retrieval workflows or costly supervised fine-tuning. We show that simply granting an off-the-shelf LLM autonomy, that is, letting it decide what to do next, already yields substantial gains even in a strict zero-shot setting. Building on this insight, we propose AT2QA, an autonomous, training-free agent for temporal question answering that iteratively interacts with the temporal knowledge graph via a general search tool for dynamic retrieval. Experiments on MultiTQ demonstrate large improvements: AT2QA achieves 88.7% Hits@1 (+10.7% over prior SOTA), including a +20.1% gain on challenging multi-target queries, showing that agentic autonomy can decisively outperform fine-tuning for temporal question answering. Code and the full set of sampled trajectories are available on https://github.com/AT2QA-Official-Code/AT2QA-Official-Code