The interesting behavior in a spin glass occurs at very low temperature, so we want to do a Monte Carlo simulation of an Ising spin glass at low T.
Suppose we adopt the usual MC approach --- generate an initial random
configuration of spins, and then start running the simulation at the
temperature T where we want to study the system. After some thermalization
time 
, the system will reach thermal equilibrium, and we can start taking
measurements as usual.
Right? Well, not exactly.