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Public transport plays an essential role in helping people escape from the congested traffic in large and crowded cities. Evaluating customer satisfaction is the key to the continuous quality improvement of public transport services. This work proposes a new public transport customer satisfaction evaluation approach based on an extended thermodynamic method with q-rung orthopair fuzzy sets. First, we use the q-ROFSs to handle the ambiguity and uncertainty of customer satisfaction evaluation information for public transport. Then, we extend the thermodynamic method to determine the customer satisfaction levels of public transport lines. Moreover, the stepwise weight assessment ratio analysis method is utilized to specify the weights of evaluation criteria as it is simple and time-saving. The effectiveness of the proposed approach is illustrated with a customer satisfaction evaluation of the rail transit network in Shanghai, China. Results showed that Line 7 has the highest customer satisfaction and Line 2 has the lowest customer satisfaction among the considered rail transit lines. Besides, nine evaluation criteria need to be optimized to improve the customer satisfaction level of Line 2 and the most critical one is train crowding. [ABSTRACT FROM AUTHOR]