1. A large number of alien plant species have been introduced as ornamental garden plants to Europe, but relatively few have become invasive. Low climatic suitability may be limiting the current invasion potential of many alien ornamental species. However, with ongoing disturbance and climate change, this barrier may be reduced for some species. 2. Here we tested how colonization ability (a prerequisite for invasion) of frequently planted alien ornamentals depends on disturbance and heating, and on their species characteristics. We sowed seeds of 37 non-naturalized alien herbaceous garden-plant species into native grassland plots with and without disturbance, and with and without infrared heating lamps. To assess whether their responses differ from those within the regional wild flora, we also sowed 14 native species and 12 naturalized alien species. During two years, we assessed the likelihoods of germination, first-year survival, second-year survival and flowering of these 63 study species. 3. The heating treatment, which also reduced soil moisture, decreased all measures of colonization success, but more so for sown native species than for the non-naturalized and naturalized alien ones. The disturbance treatment increased colonization success, and because heating decreased productivity of the undisturbed grassland plots, it also increased invasibility of these plots. Average colonization success of non-naturalized aliens was reduced by heating, but some species were not affected or performed even better with heating, particularly those with an annual life span and a high seed mass. Winter hardiness improved colonization ability of non-naturalized aliens, but this advantage was reduced in the heated plots. 4. Synthesis. Disturbance increased and heating decreased the absolute colonization success of most of the 63 species sown. However, heating had stronger adverse effects on the resident grassland and sown native species than either type of sown alien species. Together, these results suggest that some alien plants may have greater colonization success relative to native plants under a warmer climate.