The swift incorporation of artificial intelligence (AI) into the development of climate technology (Climate Tech) is producing a new category of inventions that are crucial for addressing the global climate emergency. By enhancing carbon capture technologies and creating innovative energy storage materials, AI serves as more than just a tool, functioning instead as a creative collaborator. This shift in perspective challenges the human-centered basis of patent law, introducing notable legal ambiguities concerning inventorship, ownership, and the adequacy of disclosure for AI-created environmentally friendly innovations.This paper introduces the Framework for Algorithmic-Inventive Contribution (FAIC), a novel legal and regulatory model designed to attribute patent rights for AI-driven Climate Tech innovations. The FAIC model defines inventorship using a multi-factor evaluation that considers the level and extent of human supervision, the independence of algorithms, and the origin of data. It further proposes tailored disclosure requirements, including an Algorithmic Impact Statement (AIS) and a Green Technology Efficacy Report, to ensure transparency, reproducibility, and alignment with public welfare goals.This paper investigates the economic effects of concentrated AI patent ownership on fair technology transfer to developing countries by exploring case studies in grid optimization, carbon accounting, and sustainable material science. It wraps up with a suggestion for a governance framework that includes compulsory licensing triggers aligned with climate impact metrics and a patent-term adjustment model (PTA-Green) to strike a balance between fostering innovation and addressing the critical global public good of climate change mitigation. The research asserts that patent law should transition from being purely incentive-focused to one that emphasizes stewardship, clearly acknowledging AI's pivotal role in creating a sustainable future.