When the temperature is low, the probability of accepting an inferior move (compared to the previous solution's or the "best" objective function value stored in memory - however you choose to model this), even though all constraints may be satisfied, results in an intensification of the search around a local optima which behaves similarly to hill climbing (even though the search process may be stuck and there are are no hills to climb). You can prove this to yourself by writing to file the current and "best" objective function values of an SA process (and perhaps the temperature), then graphing these. You should see that the acceptable moves (feasible solutions) along the way of the search become located closer and closer in value to the best solution as the temperature decreases. You will also likely notice that if the initial tmperature is too high, a large portion of the early part of the search is much like random search. If the initial temperature is too low, the entire process may act very similarly to hill climbing.