  We study the impact of a time-dependent external driving of the lattice
phonons in a minimal model of a BCS superconductor. Upon evaluating the
driving-induced vertex corrections of the phonon-mediated electron-electron
interaction, we show that parametric phonon driving can be used to elevate the
critical temperature $T_c$, while a dipolar phonon drive has no effect. We
provide simple analytic expressions for the enhancement factor of $T_c$.
Furthermore, a mean-field analysis of a nonlinear phonon-phonon interaction
also shows that phonon anharmonicities further amplify $T_c$. Our results hold
universally for the large class of normal BCS superconductors.
