We compute the dimuon-excess invariant mass distribution at the rho-meson peak in the context of relativistic heavy-ion collisions at Super Proton Synchrotron energies. The parameters describing the rho meson that depend on the temperature, T, and chemical potential, mu-its width, mass and leptonic decay constant-are determined from finite-energy QCD sum rules. Results show that the rho-meson width increases whereas its mass and leptonic decay constant decrease near the (chemical potential-dependent) critical temperature T(c)d(mu) for chiral symmetry restoration/quark-gluon deconfinement. As a consequence, starting from T-c(mu), for a short-lived cooling the main effect is a broadening of the dimuon distribution. However, when the evolution brings the system to a lower freeze-out temperature, with the rho-meson parameters approaching their vacuum values, the dimuon distribution shows a broad peak centered at the vacuum rho-meson mass. For even lower freeze-out temperatures the peak becomes less prominent since the thermal phase-space factor suppresses the distribution for larger values of the invariant dimuon mass, given that the average temperature is smaller. The dimuon distribution exhibits a nontrivial behavior with mu. For small mu values the distribution broadens with increasing mu becoming a bit steeper at low invariant masses for larger values of mu. Our results are in very good agreement with data from the NA60 Collaboration.