The burgeoning domain of telehealth has witnessed substantial transformation through the advent of advanced technologies such as Large Language Models (LLMs). This study examines the integration of LLMs in heart failure management, with a focus on HerzMobil as a pioneering telehealth program. The technical underpinnings of LLMs, their current applications in the medical field, and their potential to enhance telehealth services, have been explored. The paper highlights the benefits of LLMs in patient interaction, clinical documentation, and decision-making processes. Through the HerzMobil case study, improvements in patient self-management and reductions in hospital readmission rates have been observed, showcasing the successful application of telehealth in chronic disease management. The paper also delves into the challenges and ethical considerations of LLM integration, such as data privacy, potential biases, and regulatory compliance, underscoring the need for a balanced approach that prioritizes patient safety and ethical standards.