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Terrestrial insects are responding to ongoing climate change. While these responses have been primarily linked to rising temperatures, insects are sensitive to desiccation, and the impacts of altered precipitation regimes remain relatively unexplored. Here, we develop a mechanistic model of survival and performance responses to both temperature and desiccation stress, focussing on Lepidoptera in Africa, where a general understanding of such responses to climate change is urgently required. We run the model with climate data from general circulation models at daily time intervals under current (2011-2015) and projected future (2046-2050) climate scenarios. We first simulate four hypothetical, but typical, Lepidoptera that vary in thermal tolerance and developmental physiology, and then add a constraint on survival due to desiccation. Including desiccation stress leads to a 68% decline in the species range, in comparison to simulations where only species mortality due to temperature is considered. Furthermore, in response to predicted changes in both temperature and rainfall, species performances and survival are expected to change in a non-uniform manner across the landscape: species' ranges shift towards coastal regions and into higher latitudes in the southern, but not northern, hemisphere. We validate the model predictions with data from two endemic African Lepidoptera, and find that the model agrees well with their empirical distribution, but note that our model fails to account for range expansion due to water availability unrelated to rainfall (e.g. irrigation). Nonetheless, these final simulations show how the model can be readily applied to insects for which baseline physiological data already exist (or for which appropriate data can be gathered), thereby providing a useful framework with which to explore species responses to future changes in temperature and precipitation.