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Description
Ensuring spacecraft components remain within strict temperature limits depends heavily on the strategic placement and sizing of active thermal control heaters. The industry standard for this design process is manual and iterative, which is not only time-intensive but often results in suboptimal power consumption. Furthermore, while metaheuristics have been proposed for automation, they fall victim to combinatorial explosion when applied to large-scale, flight-representative models. To overcome these scalability issues, this work presents a novel optimization framework that integrates Non-Linear Programming (NLP) and Mixed-Integer Linear Programming (MILP). By leveraging the direct sensitivity method to compute exact analytical gradients, the physical properties of the Thermal Mathematical Model are directly embedded into the optimization loop to solve discrete placement and continuous power allocation under steady-state conditions. We validate this approach using the flight-representative thermal model of the ARIEL Telescope Assembly, focusing on the highly coupled decontamination heater lines of the Primary Mirror and Telescope Optical Bench. Despite evaluating a massive search space of approximately $10^{19}$ configurations, the proposed algorithm successfully identifies optimal layouts in under 10 minutes. The optimized configurations satisfy all minimum temperature constraints and significantly outperform traditional manual designs in both power efficiency and thermal gradient reduction.