Movement is critical to animal survival and, thus, biodiversity in fragmented landscapes. Increasing fragmentation in the Anthropocene necessitates predictions about the movement capacities of the multitude of species that inhabit natural ecosystems. This requires mechanistic, trait-based animal locomotion models, which are sufficiently general as well as biologically realistic. While larger animals should generally be able to travel greater distances, reported trends in their maximum speeds across a range of body sizes suggest limited movement capacities among the largest species. Here, we show that this also applies to travel speeds and that this arises because of their limited heat-dissipation capacities. We derive a model considering how fundamental biophysical constraints of animal body mass associated with energy utilisation (i.e., larger animals have a lower metabolic energy cost of locomotion) and heat-dissipation (i.e., larger animals require more time to dissipate metabolic heat) limit aerobic travel speeds. Using an extensive empirical dataset of animal travel speeds (532 species), we show that this allometric heat-dissipation model best captures the hump-shaped trends in travel speed with body mass for flying, running, and swimming animals. This implies that the inability to dissipate metabolic heat leads to the saturation and eventual decrease in travel speed with increasing body mass as larger animals must reduce their realised travel speeds in order to avoid hyperthermia during extended locomotion bouts. As a result, the highest travel speeds are achieved by animals of intermediate body mass, suggesting that the largest species are more limited in their movement capacities than previously anticipated. Consequently, we provide a mechanistic understanding of animal travel speed that can be generalised across species, even when the details of an individual species' biology are unknown, to facilitate more realistic predictions of biodiversity dynamics in fragmented landscapes.