Large language models (LLMs) are increasingly being explored in higher education, yet their effectiveness as teaching agents remains underexamined. In this paper, we present the development of GuideLM, a fine-tuned LLM designed for programming education. GuideLM has been integrated into the Debugging C Compiler (DCC), an educational C compiler that leverages LLMs to generate pedagogically sound error explanations. Previously, DCC relied on off-the-shelf OpenAI models, which, while accurate, often over-assisted students by directly providing solutions despite contrary prompting. To address this, we employed supervised fine-tuning (SFT) on a dataset of 528 student-question/teacher-answer pairs, creating two models: GuideLM and GuideLM-mini, fine-tuned on ChatGPT-4o and 4o-mini, respectively. We conducted an expert analysis of 400 responses per model, comparing their pedagogical effectiveness against base OpenAI models. Our evaluation, grounded in constructivism and cognitive load theory, assessed factors such as conceptual scaffolding, clarity, and Socratic guidance. Results indicate that GuideLM and GuideLM-mini improve pedagogical performance, with an 8% increase in Socratic guidance and a 58% improvement in economy of words compared to GPT-4o. However, this refinement comes at the cost of a slight reduction in general accuracy. While further work is needed, our findings suggest that fine-tuning LLMs with targeted datasets is a promising approach for developing models better suited to educational contexts.