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The growth of GPU-heavy data centers has increased electricity demand and challenged grid stability. This paper investigates how an energy-aware job scheduling algorithm provides flexibility in GPU-heavy data centers. We develop a rolling-horizon optimization framework considering IT power and cooling dynamics with limited future job information. Compared with the first-in first-out baseline, we show that energy-aware scheduling brings latent power flexibility during peak-price periods. This flexibility is created through both thermal and computational mechanisms: cooling shifting can reliably reduce demand for short periods at relatively low incentive (\$30/MWh), and movement of backfilled jobs can often reduce demand at similar prices (\$30-300/MWh). Further reduction is possible through reordering or delaying jobs, but due to lost profits these actions come at higher prices (starting at \$600/MWh, more significantly above \$3000/MWh). Flexibility is achievable without knowing arriving jobs, but much greater flexibility can be achieved with perfect foresight of the future queue.