Global change imposes multiple challenges on species and, thus, a reliable prediction of current and future vulnerability of species must consider multiple stressors and intrinsic traits of species. Climate, physiology, and forest cover, for example, are required to evaluate threat to thermolabile forest-dependent species, such as sloths (Bradypus spp.; Mammalia: Xenarthra). Here, we estimated future changes in the distribution of three sloth species using a metabolic-hybrid model focused on climate (climatic only, i.e., CO approach) and adding forest cover constraints to distribution of species (climate plus land cover, i.e., CL approach). We used an innovative method to generate estimates of physiological parameters for endotherms, validated with field data. The CF approach predicted a future net expansion of distribution of B. torquatus and B. variegatus, and a future net contraction of distribution of B. tridactylus. The inclusion of forest cover constraints, however, reversed the predictions for B. torquatus, with a predicted net distribution contraction. It also reduced expansion of B. variegatus, although still showing a large net expansion. Thus, B. variegatus is not predicted to be threatened in the future; B. tridactylus emerges as the species most vulnerable to climate change, but with no considerable forest losses, while B. torquatus shows the opposite pattern. Our study highlights the importance of incorporating multiple stressors in predictive models in general. To increase resilience of species to climate change, it is key to control deforestation in the Amazon for B. tridactylus, and to promote reforestation in the Atlantic Forest for B. torquatus.