Ultrafast perturbations offer a unique tool to manipulate correlated systems due to their ability to promote transient behaviors with no equilibrium counterpart. A widely employed strategy is the excitation of coherent optical phonons, as they can cause significant changes in the electronic structure and interactions on short time scales. One of the issues, however, is the inevitable heating that accompanies these resonant excitations. Here, we explore a promising alternative route: the nonequilibrium excitation of acoustic phonons, which, due to their low excitation energies, generally lead to less heating. We demonstrate that driving acoustic phonons leads to the remarkable phenomenon of a momentum-dependent effective temperature, by which electronic states at different regions of the Fermi surface are subject to distinct local temperatures. Such an anisotropic effective electronic temperature can have a profound effect on the delicate balance between competing ordered states in unconventional superconductors, opening a so far unexplored avenue to control correlated phases.