In order to predict future range shifts for invasive species it is important to explore their ability to acclimate to the new environment and understand physiological and reproductive constraints controlling their distribution. My dissertation studied mechanisms by which temperature may affect the distribution of two aggressive plant invaders in North America, Bromus tectorum and Bromus rubens. I first evaluated winter freezing tolerance of Bromus species and demonstrated that the mechanism explaining their distinct northern range limits is different acquisition time of freezing tolerance. While B. rubens has a slower rate of freezing acclimation that leads to intolerance of sudden, late-autumn drops in temperature below -12°C, B. tectorum rapidly hardens and so is not impacted by the sudden onset of severe late-autumn cold. In addition, the analysis of male reproductive development and seed production showed that neither species produces seed at or above 36°C, due to complete pollen sterility, which might trigger climate-mediated range contractions at B. tectorum and B. rubens southern margins. Finally, a detailed gas-exchange analysis combined with biochemical modelling demonstrated that both species acclimate to a broad range of temperatures and photosynthetic response to temperature does not explain their current range separation.