Invasive species pose a major threat to biodiversity and inflict massive economic costs. Effective management of bio-invasions depends on reliable predictions of areas at risk of invasion, as they allow early invader detection and rapid responses. Yet, considerable uncertainty remains as to how to predict best potential invasive distribution ranges. Using a set of mainly (sub)tropical birds introduced to Europe, we show that the true extent of the geographical area at risk of invasion can accurately be determined by using ecophysiological mechanistic models that quantify species’ fundamental thermal niches. Potential invasive ranges are primarily constrained by functional traits related to body allometry and body temperature, metabolic rates, and feather insulation. Given their capacity to identify tolerable climates outside of contemporary realized species niches, mechanistic predictions are well suited for informing effective policy and management aimed at preventing the escalating impacts of invasive species.