Climate warming is supposed to enlarge the area climatically suitable to the naturalization of alien garden plants in temperate regions. However, the effects of a changing climate on the spread of naturalized ornamentals have not been evaluated by spatially and temporarily explicit range modelling at larger scales so far. Here, we assess how climate change and the frequency of cultivation interactively determine the spread of 15 ornamental plants over the 21st century in Europe. We coupled species distribution modelling with simulations of demography and dispersal to predict range dynamics of these species in annual steps across a 250 × 250 m raster of the study area. Models were run under four scenarios of climate warming and six levels of cultivation intensity. Cultivation frequency was implemented as size of the area used for planting a species. Although the area climatically suitable to the 15 species increases, on average, the area predicted to be occupied by them in 2090 shrinks under two of the three climate change scenarios. This contradiction obviously arises from dispersal limitations that were pronounced although we assumed that cultivation is spatially adapting to the changing climate. Cultivation frequency had a much stronger effect on species spread than climate change, and this effect was non‐linear. The area occupied increased sharply from low to moderate levels of cultivation intensity, but levelled off afterwards. Our simulations suggest that climate warming will not necessarily foster the spread of alien garden plants in Europe over the next decades. However, climatically suitable areas do increase and hence an invasion debt is likely accumulating. Restricting cultivation of species can be effective in preventing species spread, irrespective of how the climate develops. However, for being successful, they depend on high levels of compliance to keep propagule pressure at a low level.