Correlative species distribution models (SDMs) are widely used to project the responses of biodiversity to global changes. The climatic niche of a species is calibrated under current climate conditions and then projected in space and/or time, making model extrapolation an important concern. This issue is particularly relevant when considering species that live at the same time at the boundaries of the current Earth’s climate and the edges of their physiological tolerance, such as desert-adapted species. To tackle these problems, alternative modelling approaches (e.g., hybrid SDMs) have been proposed. These models should explicitly consider the species’ physiological thermal tolerance, producing outputs that are closer to the species’ ecology. Here, considering mammals occurring in the Arabian Peninsula, we compared correlative SDMs with different extrapolation options (no-extrapolation, clamping, fade by clamping, full extrapolation) and hybrid SDMs incorporating the thermal tolerance of each species. We projected all models under current and future climate scenarios and measured the differences between the models’ outcomes. We found that different extrapolation options and hybrid SDMs produced important differences at least in future projections, especially for species physiologically adapted to the extreme climate conditions of the desert. Correlative SDMs blocking any extrapolations beyond the current climate conditions led to limited suitability, while SDMs allowing for extrapolations were extremely more liberal in their projections. Hybrid SDMs produced intermediate results, with up to 97% of the species losing large parts of their suitable ranges under future climate scenarios. Our findings highlight that hybrid SDMs provide a more reasonable projection of the future distribution of species that live at the edge of the current climate, given the inability of purely correlative models to track their thermal tolerances under extrapolation. For this reason, hybrid SDMs hold the premises for a better understanding of the impact of global changes on desert-adapted species.