Abstract: Large language models (LLMs) demonstrate remarkable medical expertise, but data privacy concerns impede their direct use in healthcare environments. Although offering improved data privacy protection, domain-specific small language models (SLMs) often underperform LLMs, emphasizing the need for methods that reduce this performance gap while alleviating privacy concerns. In this paper, we present a simple yet effective method that harnesses LLMs' medical proficiency to boost SLM performance in medical tasks under $privacy-restricted$ scenarios. Specifically, we mitigate patient privacy issues by extracting keywords from medical data and prompting the LLM to generate a medical knowledge-intensive context by simulating clinicians' thought processes. This context serves as additional input for SLMs, augmenting their decision-making capabilities. Our method significantly enhances performance in both few-shot and full training settings across three medical knowledge-intensive tasks, achieving up to a 22.57\% increase in absolute accuracy compared to SLM fine-tuning without context, and sets new state-of-the-art results in two medical tasks within privacy-restricted scenarios. Further out-of-domain testing and experiments in two general domain datasets showcase its generalizability and broad applicability.