To predict the response of plant pathogens to climate warming, data are needed on current thermal adaptation, the pathogen’s evolutionary potential and the link between them. We conducted a common garden experiment using isolates of the fungal pathogen Rhynchosporium commune from nine barley populations representing climatically diverse locations. Clonal replicates of 126 genetically distinct isolates were assessed for their growth rate at 12°C, 18°C and 22°C. Populations originating from climates with higher monthly temperature variation had higher growth rate at all three temperatures compared to populations from climates with less temperature fluctuation. Population differentiation in growth rate (Q_ST) was significantly higher at 22°C than population differentiation for neutral microsatellite loci (G_ST), consistent with local adaptation for growth at higher temperatures. At 18°C we found evidence for stabilizing selection for growth rate as Q_ST was significantly lower than G_ST. Heritability of growth rate under the three temperatures was substantial in all populations (0.58-0.76). Genetic variation was lower in populations with higher growth rate at the three temperatures and evolvability increased under heat stress in seven out of nine populations. Our findings imply that the distribution of this pathogen is unlikely to be genetically limited under climate warming, due to its high genetic variation and plasticity for thermal tolerance.