There is justified concern about the impact of global warming on the persistence of tropical ectotherms. There is also growing evidence for strong selection on climate-relevant physiological traits. Understanding the evolutionary potential of populations is especially important for low dispersal organisms in isolated populations, because these populations have little choice but to adapt. Despite this, direct estimates of heritability and genetic correlations for physiological traits in ectotherms—which will determine their evolutionary responses to selection—are sparse, especially for reptiles. Here we examine the heritabilities and genetic correlations for a set of four morphological and six climate-relevant physiological traits in an isolated population of an Australian rainforest lizard, Lampropholis coggeri. These traits show considerable variation across populations in this species, suggesting local adaptation. From laboratory crosses, we estimated very low to moderate heritability of temperature-related physiological traits (h2 < 0.31), but significant and higher heritability of desiccation resistance (h2~0.42). These values contrasted with uniformly higher heritabilities (h2 > 0.51) for morphological traits. At the phenotypic level, there were positive associations among the morphological traits and between thermal limits. Growth rate was positively correlated with thermal limits, but there was no indication that morphology and physiology were linked in any other way. We found some support for a specialist–generalist trade-off in the thermal performance curve, but otherwise there was no evidence for evolutionary constraints, suggesting broadly labile multivariate trait structure. Our results indicate little potential to respond to selection on thermal traits in this population and provide new insights into the capacity of tropical ectotherms to adapt in situ to rapid climate change.