One of the main problems with simulated annealing is that it is difficult to find an optimal annealing schedule, and that changing T drives the system out of equilibrium.
If we use tempering instead, the system is always in equilibrium. Also, we
can determine the temperature changes (the equivalent of the annealing
schedule) automatically, by varying the 
s so that the acceptance of
a change is 
%.
A lot of work still needs to be done in order to perfect his method.
s may be too small, a random walk in T may
not be optimal --- this all has yet to be studied in detail.