Integrated Energy Systems (IES) are an important way to improve the efficiency of energy, promote closer connections between various energy systems, and reduce carbon emissions. The transformation between electricity, heating, and cooling loads into each other makes the dynamic characteristics of multiple loads more complex and brings challenges to the accurate forecasting of multi-energy loads. In order to further improve the accuracy of IES short-term load forecasting, we propose the Convolutional Neural Network, the Long Short-Term Memory Network, and Auto-Regression (CLSTM-AR) combined with the multi-dimensional feature fusion (MFFCLA). In detail, CLSTM can extract the coupling and periodic characteristics implied in IES load data from multiple time dimensions. AR takes load data as the input to extract features of sequential auto-correlation over adjacent time periods. Then, the diverse and effective features extracted by CLSTM, LSTM, and AR can be fused using the multi-dimensional feature fusion technique. Ultimately, the model achieves the accurate prediction of multiple loads. In conclusion, compared with other forecasting models, the case study results show that MFFCLA has higher forecasting precision compared with the comparable model in the short-term multi-energy load forecasting performance of electricity, heating, and cooling. The accuracy of MFFCLA can help to optimize and dispatch IES to make better use of renewable energy.