Mechanistic species distribution models (SDMs) are ideally suited for predicting the nonnative distributions of invasive species, but require accurate parameterization of key functional traits. Importantly, any ability of the invader to acclimate or adapt rapidly to local conditions must be incorporated. Our field and laboratory studies measured phenotypic variation and tested for plasticity in the thermal sensitivity of locomotor performance and low-temperature tolerance of adult cane toads Bufo marinus in eastern Australia. We used a biophysical model to explore the adaptive significance of this variation and how it affected distribution predictions. Laboratory trials showed that geographic differences in low-temperature tolerance (i.e., the critical thermal minimum; CTMin) of field-caught toads reflect thermal acclimation, whereas populations differed in the thermal dependence of locomotor performance even after acclimation. Incorporating low-temperature tolerance as a dimension of the fundamental niche reduced the predicted southern distribution. To test whether these factors predicted to be range limiting were consistent with reduced performance for individuals, we used the biophysical model and daily climate data to conduct “virtual transplants.” These models predicted that acclimation reduced cold stress by 32–100% for toads sheltering near the ground surface; toads inside burrows could remain above their CTMin, but the required burrow depth increased with latitude. Low-temperature tolerance of the adult phase may constrain the southern range limit of the cane toad in Australia, and plasticity in this trait may have facilitated the southward range expansion.