Museums and Cultural Heritage (CH) institutions serve as crucial informal learning environments, offering opportunities for knowledge acquisition, cultural understanding, and lifelong learning outside traditional educational settings. Despite their educational potential, these institutions face significant challenges in personalizing experiences and measuring learning outcomes across diverse visitor populations. This proposal explores a novel approach to addressing these challenges by applying Large Language Models (LLMs) in CH settings. We propose a dual-role conceptual framework where LLMs are personalized guides and evaluators within museum contexts. As guides, LLMs can transform static narratives into dynamic, personalized experiences by adapting content based on visitor profiles, dwell time, and interaction patterns. As evaluators, they can generate tailored post-visit assessments that provide meaningful feedback while maintaining engagement through appropriate challenge levels. Our proposed methodology, which builds upon an existing Indoor Positioning System (IPS) deployed in a gallery, implements a theoretical three-phase approach encompassing pre-visit profiling, in-visit adaptive guidance, and post-visit assessment. This paper outlines potential implementation approaches and anticipated challenges, including LLM hallucinations and assessment validation, and proposes mitigation strategies for future empirical testing. Through this conceptual framework, we aim to address persistent issues in CH education: maintaining visitor attention, accommodating diverse learning styles, measuring learning outcomes in informal settings, and creating engaging experiences for all audience segments.