Invasive species originating from islands are released from native-range constraints such as thermal or geographic barriers. Climate matching may thus underestimate likely invasion sites for island natives. Physiological limits determine survival at thermal extremes, but rapid physiological adaptation may occur in species introduced to new environments. Leiocephalus carinatus is a lizard native to the Bahamas and Cuba and has established multiple disjunct populations in Florida, including populations north of its native range. Competing hypotheses may explain the successful invasive distribution of L. carinatus: 1) Distribution in both native and invaded ranges is constrained by the thermal conditions of the native range (Thermal Matching); 2) Distribution in the native range is constrained by geographic barriers rather than thermal conditions; lizards can tolerate environments with thermal extremes not observed in the native range (Thermal Potential); 3) Introduction to environments with differing thermal extremes leads to physiological adaptation/acclimatization to one or both extremes (Thermal Plasticity). We rejected the Thermal Matching hypothesis by comparing ecological niche models developed from the native-only range to models including invasive populations. We investigated the Thermal Potential and Thermal Plasticity hypotheses by comparing critical thermal limits of 35 L. carinatus from each of two established Florida populations, one matching latitudes in the native range, and another 160 km north of the native range. Critical thermal minima in the northern population were lower than in the south, supporting the Thermal Plasticity hypothesis for thermal minima.