Species with restricted distributions make up the vast majority of biodiversity. Recent evidence from Drosophila suggests that species with restricted distributions may simply lack genetic variation in key traits, limiting their ability to adapt to conditions beyond their current range. Specifically, tropical species of Drosophila have been shown to have low means and low genetic variation for cold tolerance and desiccation tolerance. It has therefore been predicted that these species will be limited in their response to future climatic changes. However whether these results extend beyond Drosophila is not known. We assess levels of quantitative genetic variation for cold tolerance and body size in three species of butterfly from the genus Eurema that can be classified as tropically restricted (E. laeta), tropical/subtropical (E. hecabe) and widespread (E. smilax) in their distribution. Compared to the more widely distributed species, we show that the tropically restricted E. laeta has significantly lower mean cold tolerance and lacks genetic variation for this trait. Thus, we empirically confirm in non-model organisms that low levels of genetic variation in a key ecological trait may play a role in limiting the distribution of tropically restricted species.