During public health emergencies, online rumors spread widely on social media, causing public information anxiety and emotional fluctuations. Analyzing the co-evolution patterns of online rumor themes and emotions is essential for implementing proactive and precise governance of online rumors during such events. Rumor texts from mainstream fact-checking platforms during the COVID-19 pandemic were collected and analyzed in phases based on the crisis lifecycle theory. The LDA topic model was applied to analyze the distribution of rumor themes at different stages. The Baidu AI Sentiment Analysis API was used to study the emotional tendencies of rumors at different stages. Line graphs were utilized to analyze the co-evolution characteristics of rumor themes and emotions. During the COVID-19 pandemic, the themes of online rumors can be categorized into five types: epidemic prevention and control, panic-inducing, production and livelihood, virus dissemination, and social figures. These themes exhibited repetition and fluctuation at different stages of the pandemic. The emotions embedded in pandemic-related online rumors evolved with the progression of the pandemic. Panic-inducing rumors co-evolved with negative emotions, while epidemic prevention and control rumors co-evolved with positive emotions. The study results help to understand the public's focus and emotional tendencies at different stages of the COVID-19 pandemic, thereby enabling targeted public opinion guidance and crisis management.