As neural networks (NN) are deployed across diverse sectors, their energy demand correspondingly grows. While several prior works have focused on reducing energy consumption during training, the continuous operation of ML-powered systems leads to significant energy use during inference. This paper investigates how the configuration of on-device hardware—elements such as GPU, memory, and CPU frequency, often neglected in prior studies, affects energy consumption for NN inference with regular fine-tuning. We propose PolyThrottle, a solution that optimizes configurations across individual hardware components using Constrained Bayesian Optimization in an energy-conserving manner. Our empirical evaluation uncovers novel facets of the energy-performance equilibrium showing that we can save up to 36 percent of energy for popular models. We also validate that PolyThrottle can quickly converge towards near-optimal settings while satisfying application constraints.