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The runtime behavior of Simulated Annealing (SA), similar to other metaheuristics, is controlled by hyperparameters. For SA, hyperparameters affect how temperature varies over time, and temperature in turn affects SA’s decisions on whether or not to transition to neighboring states. It is typically necessary to tune the hyperparameters ahead of time. However, there are adaptive annealing schedules that use search feedback to evolve the temperature during the search. A classic and generally effective adaptive annealing schedule is the Modified Lam. Although effective, the Modified Lam can be sensitive to the scale of the cost function, and is sometimes slow to converge to its target behavior. In this paper, we present a novel variation of the Modified Lam that we call Self-Tuning Lam, which uses early search feedback to auto-adjust its self-adaptive behavior. Using a variety of discrete and continuous optimization problems, we demonstrate the ability of the Self-Tuning Lam to nearly instantaneously converge to its target behavior independent of the scale of the cost function, as well as its run length. Our implementation is integrated into Chips-n-Salsa, an open-source Java library for parallel and self-adaptive local search.