Transcontinental dispersals by organisms usually represent improbable events that constitute a major challenge for biogeographers. By integrating molecular phylogeny, historical biogeography and palaeoecology, we test a bold hypothesis proposed by Vladimir Nabokov regarding the origin of Neotropical Polyommatus blue butterflies, and show that Beringia has served as a biological corridor for the dispersal of these insects from Asia into the New World. We present a novel method to estimate ancestral temperature tolerances using distribution range limits of extant organisms, and find that climatic conditions in Beringia acted as a decisive filter in determining which taxa crossed into the New World during five separate invasions over the past 11 Myr. Our results reveal a marked effect of the Miocene–Pleistocene global cooling, and demonstrate that palaeoclimatic conditions left a strong signal on the ecology of present-day taxa in the New World. The phylogenetic conservatism in thermal tolerances that we have identified may permit the reconstruction of the palaeoecology of ancestral organisms, especially mobile taxa that can easily escape from hostile environments rather than adapt to them.