The recent acceleration of global climate warming has created an urgent need for reliable projections of species distributions, widely used by natural resource managers. Such projections have been mainly produced by species distribution models with little information on their performances in novel climates. Here, we hindcast the range shifts of forest tree species across Europe over the last 12,000 years to compare the reliability of three different types of models. We show that in the most climatically dissimilar conditions, process-explicit models (PEMs) tend to outperform correlative species distribution models (CSDMs), and that PEM projections are likely to be more reliable than those made with CSDMs by the end of the 21st century. These results demonstrate for the first time the often promoted albeit so far untested idea that explicit description of mechanisms confers model robustness, and highlight a new avenue to increase model projection reliability in the future.