Invasions of new races can have contrasting consequences on populations of Puccinia striiformis f. sp. tritici, causing yellow rust of wheat. For example, the emergence of PstS7 (Warrior race) had major impacts in Europe and in France. By contrast, PstS2 had no impact in France, while it significantly affected other parts of the world. The objective of this study was to better understand factors that govern the success of an invasive race, taking the contrasting history of PstS7 and PstS2 in France as a case study. We compared these two races for three key factors driving invasive potential: (a) virulence against local cultivars, (b) aggressiveness in local environmental conditions, and (c) competitiveness against local races. During the period when PstS2 was detected, 70% of the grown wheat area was protected against this race by at least one known Yr resistance gene. By contrast, we found that only 15% of the wheat area had a low risk of infection by PstS7. In planta competition experiments suggested a higher competitiveness of PstS7 against local isolates compared to PstS2 in optimal thermal conditions. In silico experiments, based on thermal performance curves, suggested a high competitiveness of PstS7 considering infection efficiency. PstS2 was extremely competitive against local races in all considered environments (20 French sites x 15 years) due to its short latency period. Our findings highlight the importance of considering adaptation to environmental conditions, particularly temperature, in addition to virulence spectrum, in order to understand the evolutionary trajectories of emerging strains in pathogen populations.