Accurate prediction of the coal spontaneous combustion hazard grades is of great significance to ensure the safe production of coal mines. However, traditional coal temperature prediction models have low accuracy and do not predict the coal spontaneous combustion hazard grades. In order to accurately predict coal spontaneous combustion hazard grades, a prediction model of coal spontaneous combustion based on principal component analysis (PCA), case-based reasoning (CBR), fuzzy clustering (FM), and the snake optimization (SO) algorithm was proposed in this manuscript. Firstly, based on the change rule of the concentration of signature gases in the process of coal warming, a new method of classifying the risk of spontaneous combustion of coal was established. Secondly, MeanRadius-SMOTE was adopted to balance the data structure. The weights of the prediction indicators were calculated through PCA to enhance the prediction precision of the CBR model. Then, by employing FM in the case base, the computational cost of CBR was reduced and its computational efficiency was improved. The SO algorithm was used to determine the hyperparameters in the PCA-FM-CBR model. In addition, multiple comparative experiments were conducted to verify the superiority of the model proposed in this manuscript. The results indicated that SO-PCA-FM-CBR possesses good prediction performance and also improves computational efficiency. Finally, the authors of this manuscript adopted the Random Balance Designs—Fourier Amplitude Sensitivity Test (RBD-FAST) to explain the output of the model and analyzed the global importance of input variables. The results demonstrated that CO is the most important variable affecting the coal spontaneous combustion hazard grades.