AbstractClimate change may force organisms to adapt genetically or plastically to new environmental conditions. Invasive species show remarkable potential for rapid adaptation. The ovoviviparous New Zealand mud snail (NZMS),Potamopyrgus antipodarum, has successfully established across Europe with two clonally reproducing mitochondrial lineages since its arrival in the first half of the 19th century. Its remarkable variation in shell morphology was shown to be fitness relevant. We investigated the effects of temperature on shell morphology across 11 populations from Germany and the Iberian Peninsula in a common garden across three temperatures. We analyzed size and shape using geometric morphometrics. For both, we compared reaction norms and estimated heritabilities. For size, the interaction of temperature and haplotype explained about 50% of the total variance. We also observed more genotype by environment interactions indicating a higher degree of population differentiation than in shape. Across the three temperatures, size followed the expectations of the temperature‐size rule, with individuals growing larger in cold environments. Changes in shape may have compensated for changes in size affecting space for brooding embryos. Heritability estimates were relatively high. As indicated by the very low coefficients of variation for clonal repeatability (CVA), they can probably not be compared in absolute terms. However, they showed some sensitivity to temperature, in haplotype t more so than in z, which was only found in Portugal. The lowCVAvalues indicate that genetic variation among European populations is still restricted with a low potential to react to selection. A considerable fraction of the genetic variation was due to differences between the clonal lineages. The NZMS has apparently not been long enough in Europe to accumulate significant genetic variation relevant for morphological adaptation. As temperature is obviously not the sole factor influencing shell morphology, their interaction will probably not be a factor limiting population persistence under a warming climate in Europe.