Recently, we showed that plasmon-exciton coupling can increase entropy current through a bridge coupled to plasmonic metal nanoparticles. Here we show that electron-phonon coupling can also be used to control the entropy current in similar systems. Entropy current tends to decrease due to electron-phonon coupling and to exhibit a monotonous decrease upon temperature ramping. However, an anomaly affecting the current where it is enhanced by electron-phonon coupling is indicated at around 42 times the system's Kondo temperature. We therefore report means to control heat flow by tuning the Kondo resonance through the electron-phonon coupling. We analyze the conditions that bring about these trends due to electron-phonon coupling by employing non-equilibrium Green's function formulation addressing the entropy current and the derived heat flow.