The recent development of human societies has led to major, rapid, and often inexorable changes in the environment of most animal species. Over the last decades, a growing number of studies formulated predictions on the modalities of animal adaptation to novel or changing environments, questioning how and at what speed animals should adapt to such changes, discussing the levels of risks imposed by changes in the mean and/or variance of temperatures on animal performance, and exploring the underlying roles of phenotypic plasticity and genetic inheritance. These fundamental predictions, however, remain poorly tested using field data. Here, we tested these predictions using a unique continental‐scale data set in the European earwig Forficula auricularia L., a univoltine insect introduced in North America one century ago. We conducted a common garden experiment, in which we measured 13 life‐history traits in 4,158 field‐sampled earwigs originating from 19 populations across North America. Our results first demonstrate that 10 of the 13 measured life‐history traits are associated with two sets of variations in seasonal temperatures, that is, winter–summer and autumn–spring. We found, however, no association with the overall mean monthly temperatures of the invaded locations. Furthermore, our use of a common garden setup reveals that the observed patterns of variation in earwigs’ life‐history traits are not mere plastic responses to their current environment, but are either due to their genetic background and/or to the environmental conditions they experienced during early life development. Overall, these findings provide continent‐scale support to the claims that adaptation to thermal changes can occur quickly (in less than 100 generations), even in insects with long life cycles, and emphasize the importance of variation in seasonal temperature over mean population temperatures in climate adaptation.