Why does the nitrogen tetroxide and nitrogen dioxide mixture reach a new equilibrium after a temperature change?

The mixture of nitrogen tetroxide ($N_2{O}_4$) and nitrogen dioxide ($N{O}_2$) reaches a new equilibrium after a temperature change because the system acts to counteract the disturbance, as described by Le Chatelier's principle.

At any given temperature and pressure, the ratio of dimers ($N_2{O}_4$) to monomers ($N{O}_2$) is constant because the rate of dissociation is exactly balanced by the rate of association. When the temperature is altered, the reactivities of the monomer and dimer change instantaneously, shifting the chemical equilibrium constant.12

Because the system cannot respond instantaneously, the concentrations of the species adjust at a finite rate—a process known as chemical relaxation. During this time, the system undergoes a net change in composition until the association and dissociation rates are rebalanced to suit the new temperature conditions. The speed at which this new equilibrium is reached is limited by the concentrations and reactivities of the molecules involved.1