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Transient simulations are widely used in studying the past climate as they provide better comparison with any exisiting proxy data. However, multi-millennial transient simulations using coupled climate models are usually computationally very expensive. As a result several acceleration techniques are implemented when using numerical simulations to recreate past climate. In this study, we compare the results from transient simulations of the present and the last interglacial with and without acceleration of the orbital forcing, using the comprehensive coupled climate model CCSM3 (Community Climate System Model 3). Our study shows that in low-latitude regions, the simulation of long-term variations in interglacial surface climate is not significantly affected by the use of the acceleration technique (with an acceleration factor of 10) and hence, large-scale model-data comparison of surface variables is not hampered. However, in high-latitude regions where the surface climate has a direct connection to the deep ocean, e.g. in the Southern Ocean or the Nordic Seas, acceleration-induced biases in sea-surface temperature evolution may occur with potential influence on the dynamics of the overlying atmosphere. The data provided here are from both accelerated and non-accelerated runs as decadal mean values.