Recent advances in Chain-of-Thought (CoT) prompting have substantially enhanced the reasoning capabilities of large language models (LLMs), enabling sophisticated problem-solving through explicit multi-step reasoning traces. However, these enhanced reasoning processes introduce novel attack surfaces, particularly vulnerabilities to computational inefficiency through unnecessarily verbose reasoning chains that consume excessive resources without corresponding performance gains. Prior overthinking attacks typically require restrictive conditions including access to external knowledge sources for data poisoning, reliance on retrievable poisoned content, and structurally obvious templates that limit practical applicability in real-world scenarios. To address these limitations, we propose POT (Prompt-Only OverThinking), a novel black-box attack framework that employs LLM-based iterative optimization to generate covert and semantically natural adversarial prompts, eliminating dependence on external data access and model retrieval. Extensive experiments across diverse model architectures and datasets demonstrate that POT achieves superior performance compared to other methods.