Climate change and habitat destruction are two of the greatest threats to global biodiversity. Lattice models have been used to investigate how hypothetical species with different characteristics respond to habitat loss. The main result shows that a sharp threshold in habitat availability exists below which a species rapidly becomes extinct. Here, a similar modelling approach is taken to establish what determines how species respond to climate change. A similar threshold exists for the rate of climate change as has been observed for habitat loss—patch occupancy remains high up to a critical rate of climate change, beyond which species extinction becomes likely. Habitat specialists, especially those of relatively poor colonizing ability are least able to keep pace with climate change. The interaction between climate change and habitat loss might be disastrous. During climate change, the habitat threshold occurs sooner. Similarly, species suffer more from climate change in a fragmented habitat.