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It has been well recognized that, for most climatic records, their current states are influenced by both past conditions and current dynamical excitations. However, how to properly use this idea to improve the climate predictive skills, is still an open question. In this study, we evaluated the decadal hindcast experiments of 11 models (participating in phase 5 of the Coupled Model Intercomparison Project, CMIP5) in simulating the effects of past conditions (memory part, M(t)) and the current dynamical excitations (non-memory part, epsilon(t)). Poor skills in simulating the memory part of surface air temperatures (SAT) are found in all the considered models. Over most regions of China, the CMIP5 models significantly overestimated the long-term memory (LTM) of SAT. While in the southwest, the LTM was significantly underestimated. After removing the biased memory part from the simulations using fractional integral statistical model (FISM), the remaining non-memory part, however, was found reasonably simulated in the multi-model means. On annual scale, there were high correlations between the simulated and the observed epsilon(t) over most regions of the country, and for most cases they had the same sign. These findings indicated that the current errors of dynamical models may be partly due to the unrealistic simulations of the impacts from the past. To improve predictive skills, a new strategy was thus suggested. As FISM is capable of extracting M(t) quantitatively, by combining FISM with dynamical models (which may produce reasonable estimations of epsilon(t)), improved climate predictions with the effects of past conditions properly considered may become possible.