Abstract: As a result of climate change, many populations have to modify their range to follow the suitable areas—their “climate envelope”—often risking extinction. During this migration process, they may face absolute boundaries to dispersal because of external environmental factors. Consequently, not only the position, but also the shape of the climate envelope can be modified. We use a reaction-diffusion model to analyse the effects on population persistence of simultaneous changes in the position and shape of the climate envelope. When the growth term is of logistic type, we show that extinction and persistence are principally conditioned by the species mobility and the speed of climate change, but not by the shape of the climate envelope. However, with a growth term taking an Allee effect into account, we find a high sensitivity to variations in the shape of the climate envelope. In this case, the species which have a high mobility, although they could more easily follow the migration of the climate envelope, would be at risk of extinction when encountering a local narrowing of the boundary geometry. This effect can be attenuated by a progressive opening at the exit of the narrowing into the available space, even though this leads temporarily to a diminished area of the climate envelope.