The two non-native grasses that have established long-term populations in Antarctica (Poa pratensis and Poa annua) were studied from a global multidimensional thermal niche perspective to address the biological invasion risk to Antarctica. These two species exhibit contrasting introduction histories and reproductive strategies and represent two referential case studies of biological invasion processes. We used a multistep process with a range of species distribution modelling techniques (ecological niche factor analysis, multidimensional envelopes, distance/entropy algorithms) together with a suite of thermoclimatic variables, to characterize the potential ranges of these species. Their native bioclimatic thermal envelopes in Eurasia, together with the different naturalized populations across continents, were compared next. The potential niche of P.��pratensis was wider at the cold extremes; however, P.��annua life history attributes enable it to be a more successful colonizer. We observe that particularly cold summers are a key aspect of the unique Antarctic environment. In consequence, ruderals such as P.��annua can quickly expand under such harsh conditions, whereas the more stress-tolerant P.��pratensis endures and persist through steady growth. Compiled data on human pressure at the Antarctic Peninsula allowed us to provide site-specific biosecurity risk indicators. We conclude that several areas across the region are vulnerable to invasions from these and other similar species. This can only be visualized in species distribution models (SDMs) when accounting for founder populations that reveal nonanalogous conditions. Results reinforce the need for strict management practices to minimize introductions. Furthermore, our novel set of temperature-based bioclimatic GIS layers for ice-free terrestrial Antarctica provide a mechanism for regional and global species distribution models to be built for other potentially invasive species.