Climate change and biological invasions are two major global environmental challenges. Both may interact, e.g. via altered impact and distribution of invasive alien species. Even though invasive species play a key role for compromising the health of honey bees, the impact of climate change on the severity of such species is still unknown. The small hive beetle (SHB, Aethina tumida, Murray) is a parasite of honey bee colonies. It is endemic to sub-Saharan Africa and has established populations on all continents except Antarctica. Since SHBs pupate in soil, pupation performance is governed foremost by two abiotic factors, soil temperature and moisture, which will be affected by climate change. Here, we investigated SHB invasion risk globally under current and future climate scenarios. We modelled survival and development time during pupation (=pupal performance) in response to soil temperature and soil moisture using published and novel experimental data. Presence data on SHB distribution were used for model validation. We then linked the model with global soil data in order to classify areas (resolution: 10 arcmin; i.e. 18.6 km at the equator) as unsuitable, marginal and suitable for SHB pupation performance. Under the current climate, the results show that many areas globally yet uninvaded are actually suitable, suggesting considerable SHB invasion risk. Future scenarios of global warming project a vehement increase in climatic suitability for SHB and corresponding potential for invasion, especially in the temperate regions of the Northern hemisphere, thereby creating demand for enhanced and adapted mitigation and management. Our analysis shows, for the first time, effects of global warming on a honey bee pest and will help areas at risk to prepare adequately. In conclusion, this is a clear case for global warming promoting biological invasion of a pest species with severe potential to harm important pollinator species globally.