In the evolution of an emergency, Internet public opinions usually catalyze escalation and spread of the emergency, and even affect the evolution of public opinions. Therefore, how to effectively manage Internet public opinions has become urgent. As an essential part of the Internet public opinion management, assessing the heat degree of Internet public opinions is necessary. Being problem-oriented, this paper analyzes the development and evolution of Internet public opinions, and identifies the characteristics of the heat degree assessment of Internet public opinions. Taking into account the continuously changing exterior environment, the dynamic nature of Internet public opinions, and the inadequacy and uncertainty of decision-making information, assessing the heat degree of Internet public opinions is regarded as a dynamic multi-attribute decision making problem under the probabilistic linguistic environment. Thus, this paper aims to develop a dynamic decision-making framework to assess the heat degrees of Internet public opinions under the probabilistic linguistic environment. First, the probabilistic linguistic Bayesian network (PLBN) is constructed, in which the nodes denote attributes and related factors, and the hierarchical network structure shows the relationship among attributes. Then, the probability information obtained by PLBN in the form of PLTS is converted into attribute weight information. Moreover, this paper starts from the nature of PLTS, discusses PLTSs in terms of the probability distribution, and then gives the concept of the dominance degree of PLTS, based on which, a dynamic decision-making model based on the idea of prospect theory that considers DMs’ bounded rationality is developed. Finally, five emergency events happened in China are selected as a case to illustrate the proposed approach and some analyses and discussions have been carried out to verify the validity of our approach.