Dear Kiarash,
You are totally right: this is a mistake. The cases "beta small" and "beta large" should be reversed in the sentence.
"beta small" means "high temperature regime" (beta=1/T) [therefore the confusion in the solutions, probably]: the chain visits the states nearly uniformly, and doesn't settle, or settles with low probability in the minimum of f
"beta large" means "low temperature regime": the chain barely moves, because of the low acceptance probabilities in this regime) and gets stuck in local minima of f
All the best,
Olivier
