Global warming not only can affect the insects directly, but in some cases (see case of the monarch butterflies, Danaus plexippus, in the following article) also indirectly, by affecting their larval foodplants (it causes chemical changes to them and turns them into poison for the caterpillars which feed on them)..
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Another example is the well-known mountain butterfly Parnassius apollo (Lepidoptera: Papilionidae). Global warming causes not only decline in its populations, but also a shift to higher elevation.
Article Response of Parnassius apollo population and vertical distri...
Additional comments by me: In relatively low mountains in Europe, where the shift to higher elevation is not possible, this species has already become extinct or is threatened with extinction, in contrast to the nice situation here in Greece, where we have high mountains, and this species is still abundant, as global warming hasn't affected its open grassland habitat. When global warming affects its habitats at lower altitudes, grasslands are being overgrown by high vegetation and forests, then the caterpillars, which feed on the very close to the ground growing Sedum spp., can't find easily (or at all) the foodplant, as the female butterflies are forced to lay their eggs elsewhere due to habitat overgrowth. Thus, they shift to higher elevations of open grassland habitats to survive, but this is not possible when the mountain is not high enough..
Global warming also affects the synchrony between the end of diapause of the caterpillars and the phenology of Sedum foodplant..
Conference Paper Decreasing elevational range of Parnassius apollo in the nor...
Another study shows that habitat overgrowth due to global warming isolates the populations of Parnassius butterflies in Canadian Rocky Mts., which may lead to extinction..
In the case of, for example, Parnassius apollo which I mentioned above, grazing helps, as it keeps the habitat open and prevents overgrowth. However, it is known that over-grazing threatens many species with extinction.
I should also add that, in contrast to the negative effect mentioned in my previous answer, in some other cases, global warming can help some insect species to spread their range. Examples: