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In this paper we study the design of aperiodic servers in thermally constrained real-time systems. We start by illustrating how naive slack stealing leads to missed deadlines in the presence of speed-control-based dynamic thermal management. We then proceed to describe a design time execution-budget allocation scheme that takes advantage of the predictable thermal behavior of the system to control the execution of aperiodic workload. We introduce the transient overclocking server, which safely reduces the response time for aperiodic jobs in the presence of hard real-time periodic tasks and thermal constraints. We show by simulation that the transient overclocking server works well under thermal constraints of the system, and that there is an optimal budget allocation that depends on the temporal characteristics of the aperiodic tasks.