Education for sustainable development (ESD) of protected areas is proposed to deal with global climate change and biodiversity conversation. It focuses on the “quality education” and “protection” of the United Nations’ sustainable development goals (UN SDGs), not only taking protected areas as the education place, but also as the theme and content of education. Based on cognitive-behavior theory and social emotional learning theory, this study constructs a “cognitive–emotion–behavior” dimension framework of ESD in protected areas, selecting Potatso National Park in Yunnan as a case study. Based on 529 valid visitor questionnaires, this study uses structural equation modeling to verify theoretical hypotheses, and analyzes the impact of ESD in protected areas on public cognition, emotion, and behavior. The results show that: (1) Cognitive and emotional factors jointly drive the behavioral intentions of ESD in protected areas, and social-emotional factors are slightly higher than cognitive factors; (2) Environmental knowledge, personal norms, nature connectedness, and places attachment positively affects behavioral intentions; (3) Indigenous knowledge has an impact on behavioral intentions through emotional mediation, and personal norms have an impact on behavioral intentions through direct effects; (4) Gender and visit frequency are important moderating variables in the ESD of protected areas. These conclusions provide the following suggestions for further development of ESD. First, by forming environment-friendly social norms and focusing on the mining and presentation of indigenous knowledge, the behavioral intention can also be enhanced to a certain extent; second, improving people’s emotion can also promote people’s behavioral intention, especially referring to optimizing nature connectedness, strengthening place attachment, and creating emotional connections; Third, specific groups of people should be taught specifically, and improve the supporting services of ESD.
