Heat generation in exothermic reactions
Unlike the other factors affecting chemical equilibrium, (namely concentration, pressure), temperature follows the Le Chatelier principle via a different mechanism.

Temperature alters the equilibrium constant $K$, and this change in $K$ also changes the relative concentrations of the reactants and the products. The way in which the equilibrium constant depends on temperature is given by Van't Hoff equation:
$$\frac{d \ln K}{d T}=\frac{\Delta H}{RT^2}$$
Therefore, for exothermic reactions, the change in $K$ acts as if heat is one of the products, since increasing the temperature causes the $K$ to decrease, making the equilibrium at lower temperatures more favorable for Haber's process for making ammonia. (While this only talks of the equilibrium concentrations, lower temperatures in general result in slower rates, hence a balance is always sought)

While for your other question, as the temperature increases, the equilibrium is reached faster by both increasing ammonia (the cause of the increasing temperatures) and the decreasing $K$, until at a certain temperature, the reaction reaches equilibrium. I am not sure of the practical constraints employed in temperature regulation in the industry.