Here we provide a physical and mathematical framework for the description of flow-driven oscillators. These oscillators, differently from frequency-driven harmonic systems, are based on countercurrent mass flows and thermal-energy exchange. We describe this class of oscillators through two countercurrent fluids separated by a heated conductive medium. We show how this configuration embeds the essential elements of harmonic oscillators, such as resonance condition, periodic orbits, and quality factor or decay time. The key advantage of recognizing flow-driven systems as oscillators lies in the possibility to engineer them according to the properties of resonant systems and utilize them to control their temperature, maximize the stored energy, or coupling them in networks. We report examples of simple configurations at their resonant condition, enhancing both thermal energy and decay time by factors larger than 10. We finally show two flow-driven oscillators coupled in series, featuring a reconfigurable internal temperature distribution, depending on the selected resonant condition.