Flow Cell Arrays (FCA) technology employs microchannels filled with an electrolytic fluid to concurrently provide cooling and power generation to integrated circuits (ICs). This solution is particularly appealing for Three-Dimensional Multi-Processor Systems-on-Chip (3D MPSoCs) realized in deeply scaled technologies, as their extreme power densities result in significant thermal and voltage supply challenges. FCAs provide them with an extra power budget to boost their performance. However, the dual effects of FCAs (cooling and power supply) have conflicting trends, leading to a complex interplay between temperature, voltage stability, and performance. In this paper, we explore this trade-off by introducing a novel methodology that controls the operating frequency of computing components and the electrolytic coolant flow rate at run-time. Our strategy enables tangible performance gains while abiding by timing, voltage drop, and temperature constraints. We showcase its benefits by targeting a 4-layer 3D MPSoC platform, achieving up to 24% increase in the operating frequencies and resulting in application speedups of up to 17%, while at the same time reducing the costs related to FCA liquid pumping energy.