Invasive plant species pose a major threat to biodiversity and the essential role that biodiversity plays in the functioning of ecosystems, therefore it is necessary to understand the mechanisms behind the spread of invasive plants. A number of studies have shown that a large number of factors (e.g. an increased competitive capacity) can be responsible for the success of a species in the invasion process, and that temperature extremes are often a major obstacle to plant propagation. To better understand the case of the windmill palm in southern Switzerland in particular, we measured the photosynthetic performance, heat tolerance, and cold hardiness of several native and introduced evergreen species during the deacclimation period, i.e. between January and April. Contrary to what we hypothesised, we found that the invasiveness of exotic species was not linked to higher photosynthetic performance in winter or spring. We also found that the structural changes involved in higher heat tolerance or cold hardiness do not compromise the photosynthetic performance of the species studied. In addition, the propagation of these species is currently not limited by their frost resistance, particularly in the case of the windmill palm. So other factors, such as propagule pressure, are certainly contributing to the success of the windmill palm invasion in southern Switzerland, which continues to threaten local biodiversity.