Why is the Haber Process run at 450 °C instead of room temperature?

the forward reaction of the harbour process is exothermic, it gives out heat. so increasing temperature  will shift the equilibrium and decrease the yeild, however increasing the temperature also increases the rate of reaction.

All chemical processes have to compromise between  high rate and high yeild to give the most economical conditions. in this case the high rate turns out to be more economical so a high temerature is used.