Arctic Ocean sea ice proxies generally suggest a reduction in sea ice during parts of the early and middle Holocene (∼6000–10,000 years BP) compared to present day conditions. This sea ice minimum has been attributed to the northern hemisphere Early Holocene Insolation Maximum (EHIM) associated with Earth's orbital cycles. Here we investigate the transient effect of insolation variations during the final part of the last glaciation and the Holocene by means of continuous climate simulations with the coupled atmosphere–sea ice–ocean column model CCAM. We show that the increased insolation during EHIM has the potential to push the Arctic Ocean sea ice cover into a regime dominated by seasonal ice, i.e. ice free summers. The strong sea ice thickness response is caused by the positive sea ice albedo feedback. Studies of the GRIP ice cores and high latitude North Atlantic sediment cores show that the Bølling–Allerød period (c. 12,700–14,700 years BP) was a climatically unstable period in the northern high latitudes and we speculate that this instability may be linked to dual stability modes of the Arctic sea ice cover characterized by e.g. transitions between periods with and without perennial sea ice cover.