Temperature as an important indicator of climate change, accurate temperature prediction has important guidance and application value for agricultural production, energy management and disaster warning. Based on the advantages of CEEMDAN model in effectively extracting the time–frequency characteristics of nonlinear and nonsmooth signals, BO algorithm in optimizing the objective function within a limited number of iterations, and BiLSTM model in revealing the connection between the current data, the previous data and the future data, a monthly average temperature prediction model based on CEEMDAN–BO–BiLSTM is established. A CEEMDAN–BO–BiLSTM-based monthly average temperature prediction model is developed and applied to the prediction of monthly average temperature in Jinan City, Shandong Province. The results show that the constructed monthly mean temperature prediction model based on CEEMDAN–BO–BiLSTM is feasible; the constructed CEEMDAN–BO–BiLSTM model has an average absolute error of 1.17, a root mean square error of 1.43, an average absolute percentage error of 0.31%, which is better than CEEMDAN–BiLSTM, EMD–BiLSTM, and BiLSTM models in terms of prediction accuracy and shows better adaptability; the constructed CEEMDAN–BO–BiLSTM model illustrates that the model is not over-modeled and adds complexity using Friedman’s test and performance comparisons between model run speeds. The model provides insights for effective forecasting of monthly mean temperatures.