Although the impacts of climate change and invasive species are typically studied in isolation, they likely interact to reduce the viability of plant and animal populations. Indeed, invasive species, by definition, have succeeded in areas outside of their native range and may therefore have higher adaptive capacity relative to native species. Nevertheless, the genetic architecture of the thermal niche, which sets a limit to the potential for populations to evolve rapidly under climate change, has never been measured in an invasive species in its introduced range. Here, we estimate the genetic architecture of thermal performance in the harlequin beetle (Harmonia axyridis), a Central Asian species that has invaded four continents. We measured thermal performance curves in more than 400 third‐generation offspring from a paternal half‐sib breeding experiment and analyzed the genetic variance–covariance matrix. We show that while the critical thermal limits in this species have an additive genetic basis, most components of the thermal performance curve have low heritability. Moreover, we found evidence that genetic correlations may constrain the evolution of beetles under climate change. Our results suggest that some invasive species may have limited evolutionary capacity under climate change, despite their initial success in colonizing novel environments.