In order to avoid the metastable states produced by quenching, metals are often cooled very slowly, which allows them time to order themselves into stable, structurally strong, low energy configurations. This is called annealing.
Annealing gives the system the opportunity to jump out of local minima with a reasonable probability while the temperature is still relatively high.
We can adopt the same approach in Monte Carlo simulations. We start with a random configuration at a very high temperature, and then reduce the temperature ``very slowly'' until we reach the desired low temperature. This should result in a thermalized configuration.