Thematic Analysis (TA) is a widely used qualitative method that provides a structured yet flexible framework for identifying and reporting patterns in clinical interview transcripts. However, manual thematic analysis is time-consuming and limits scalability. Recent advances in LLMs offer a pathway to automate thematic analysis, but alignment with human results remains limited. To address these limitations, we propose SFT-TA, an automated thematic analysis framework that embeds supervised fine-tuned (SFT) agents within a multi-agent system. Our framework outperforms existing frameworks and the gpt-4o baseline in alignment with human reference themes. We observed that SFT agents alone may underperform, but achieve better results than the baseline when embedded within a multi-agent system. Our results highlight that embedding SFT agents in specific roles within a multi-agent system is a promising pathway to improve alignment with desired outputs for thematic analysis.