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Correlative ecological niche models are increasingly used to estimate potential distributions during the Last Glacial Maximum (LGM) for biogeographical research. In the case of presence-background/pseudoabsences techniques, cold environments that are poorly represented in existing geography can complicate the process of model calibration and transfer into more extreme cold environments that were very common during the LGM (non-analog conditions). This may lead to biologically unrealistic estimations. Using one cold-adapted North American mammal, we explore a real scenario to better understand the effect of restricting the range of environmental conditions over which niche models are calibrated and then transferred to LGM conditions. We performed two sets of experiments in Maxent: 1) we calibrated models in the context of only present-day climate conditions, which is the most common practice, and compared predictions under LGM conditions based on two extrapolation methods (clamping versus unconstrained); 2) we calibrated single models using both present-day and LGM conditions as part of the same background in order to include more extreme environments in the model calibration. Our experiments led to dramatically different estimates of species' potential distributions, showing notable differences with respect to latitudinal and elevational shifts during the LGM. Models calibrated using present-day climates yielded biologically unrealistic estimations, suggesting that species survived in the glaciers during the LGM. Even more unrealistic estimations were achieved when clamping was enforced as the method to extrapolate. Models calibrated in the context of both modern and past climates reduced the required degree of extrapolation and allowed more realistic potential distributions, suggesting that the species avoided extremely cold conditions during the LGM. This study alerts to the possibility of obtaining implausible potential distributions during the LGM due to restricted background datasets and offers recommendations that should promote better strategies to estimate distributional changes during glaciations.