High water temperatures can increase the energetic cost for salmon to migrate and spawn, which can be important for Snake River fall‐run Chinook salmon because they migrate great distances (>500 km) at a time when river temperatures (18–24°C) can be above their optimum temperatures (16.5°C). Average river temperatures and random combinations of migration and spawning dates were used to simulate fish travel times and determine the energetic consequences of different thermal experiences during migration. An energy threshold criterion (4 kJ/g) was also imposed on survival and spawning success, which was used to determine how prevailing temperatures might select against certain migration dates and thermal experiences, and in turn, explain the selection for the current spawning phenology of the population. Scenarios of tributary use for thermal refugia under increasing water temperatures (1, 2, and 3°C) were also run to determine which combinations of migration dates, travel rates, and resulting thermal experiences might be most affected by energy exhaustion. As expected, when compared to observations, the model under existing conditions and energy use could explain the onset, but not the end of the observed spawning migration. Simulations of early migrants had greater energy loss than late migrants regardless of the river temperature scenario, but higher temperatures disproportionately selected against a larger fraction of early‐migrating fish, although using cold‐water tributaries during migration provided a buffer against higher energy use at higher temperatures. The fraction of simulated fish that exceeded the threshold for migration success increased from 58% to 72% as average seasonal river temperatures over baseline temperatures increased. The model supports the conclusion that increases in average seasonal river temperatures as little as 1°C could impose greater thermal constraints on the fish, select against early migrants, and in turn, truncate the onset of the current spawning migration.