Many threatened species depend on climatic microrefugia, but places with harsh climates for predators may also play a refugial role. Feral cats threaten many native species in arid Australia. Although cats can persist in regions with no free water, their abundance should depend on the availability of microclimates that protect them from harsh environmental conditions. We developed a biophysical model of feral cat heat stress and used it to explore how behavior and microhabitat features influence water requirements and activity. Tests of model predictions against fine‐scale GPS and microclimate data highlight the importance of refuges, particularly rabbit burrows. Continent‐wide simulations show large but temporally varying areas of the arid zone that would be lethal for cats without access to deep or shaded burrows. Our approach can identify locations that may act as natural refuges for native prey, and where habitat management strategies may be effective in controlling cat abundance.