Scientific consensus has confirmed that that the ongoing increase in average global temperature poses manifold threats to humanity. Despite suggestions to the contrary, the effects of changes in the Earth’s climate on human mobility and cross-border migration are still unclear, especially with regard to migration to Europe. Attempts to coin the term ‘climate refugee’ suggest the need to expand the scope of the 1951 Refugee Convention, as the existing definition of a refugee does not cover climate change. We argue that attempts to widen the scope of the Convention would end up in failure, and even if they succeeded, the inclusion of climate change would damage the international protection regime.