1. The ranges of many species have expanded in cool regions but contracted at warm margins in response to recent climate warming, but the mechanisms behind such changes remain unclear. Particular debate concerns the roles of direct climatic limitation vs. the effects of interacting species in explaining the location of low latitude or low elevation range margins. 2. The mountains of the Sierra de Guadarrama (central Spain) include both cool and warm range margins for the black-veined white butterfly, Aporia crataegi, which has disappeared from low elevations since the 1970s without colonizing the highest elevations. 3. We found that the current upper elevation limit to A. crataegi's distribution coincided closely with that of its host plants, but that the species was absent from elevations below 900 m, even where host plants were present. The density of A. crataegi per host plant increased with elevation, but overall abundance of the species declined at high elevations where host plants were rare. 4. The flight period of A. crataegi was later at higher elevations, meaning that butterflies in higher populations flew at hotter times of year; nevertheless, daytime temperatures for the month of peak flight decreased by 6.2 degrees C per 1 km increase in elevation. 5. At higher elevations A. crataegi eggs were laid on the south side of host plants (expected to correspond to hotter microclimates), whereas at lower sites the (cooler) north side of plants was selected. Field transplant experiments showed that egg survival increased with elevation. 6. Climatic limitation is the most likely explanation for the low elevation range margin of A. crataegi, whereas the absence of host plants from high elevations sets the upper limit. This contrasts with the frequent assumption that biotic interactions typically determine warm range margins, and thermal limitation cool margins. 7. Studies that have modelled distribution changes in response to climate change may have underestimated declines for many specialist species, because range contractions will be exacerbated by mismatch between the future distribution of suitable climate space and the availability of resources such as host plants.