Our paper uses a general equilibrium framework to examine the effects of temperature on firm-level demand, productivity and input allocative efficiency. Using data from Italian firms and detailed climate data, it uncovers a sizeable negative effect of extreme temperatures on firm-level productivity. Based on these estimates, the model generates aggregate productivity losses from local temperature fluctuations that are higher than previously thought, ranging from 0.60% to 6.82% depending on the scenario and the extent of adaptation. Notably, these losses are approximately four times greater than those estimated by averaging firm-level losses in a representative firm model, which does not capture frictions that alter allocative efficiency across firms. Therefore, incorporating our framework into Integrated Assessment Models is likely to increase the estimated economic costs of climate change.